1) Personally I think it is admirable for a person of faith to seek to rationalise his beliefs in this fashion. But…
2) In the Wittgenstenian paradigm of language I am sceptical that in the absence of direct, observable, testable God-Phenomena science has the conceptual framework to ‘prove’ (and by extension ‘disprove’) God. And…
3) Such seeking of Phenomena i.e. the ‘created order’ of the world etc., and the struggle to infer ‘proof’ or ‘disproof’ from this evidence is to misunderstand or misattribute natural-phenomena and God=phenomena… But…
4) Pantheism or Panentheism would be an alternative and I suspect that all attempts at a scientific understanding of God must lead towards that kind of theology (and that is not the God of Christianity – who says thats the God anyway?!)… Furthermore…
5) Lennox’s aim is to find ‘evidence’ which is the highest valued currency for scientists (i.e. Dawkins)… but Lennox is a Christian who happens to be a scientist* and therefore falls unfortunately into Dawkins criteria of inadmissability – he believes and looks for supporting evidence as opposed to observing phenomenological evidence and inferring a reason to believe… * I may have misjudged Lennox, he may have converted because of evidence but this only renders ‘his evidence’ subjective interpretation and an a priori agnostic/atheist such as Dawkins may refuse to interpret the natural-phenomena as God-phenomena.

So my opinion is that Lennox is a well meaning justifiar or apologist – but his rational-value is probably worthy and convincing only to other theists. In this respect he is similar to Anselm: Faith seeking Understanding.
In which case – contrary to the Dawkins paradigm of knowledge – evidence is not a primary source it is reinforcement of the God-hypothesis.

The real key is in analysing the God-hypothesis – the idea of God. At this point Wittgenstein and indeed most of the Great Mystics wade back into the argument – can one fully concieve of ‘omnipotence’, ‘omniscience’ and the ‘infinite’ or can one only allude to it?
As Wittgenstein might say the God-phenomena can only “show itself”, its ineffable ‘parameters’ defy the parameters of language and expression – thus always rendering the God-hypothesis a poor second to the God-phenomena.

In this case then two questions emerge:
1) Can I honestly hold to the God-hypothesis if I have never experienced (or interpreted an experience to be of) the God-phenomena? and
2) In this paradigm of silence should organised religion/ritual have a place?

The answer to (1) has two categories. Firstly trust in the interpretation of the experience of the higher mystics – and we really only ever have their word – and maybe now neurological testing but even that only shows a hightened state of mental activity – that something is at least thought to be experienced. And secondly the fraction of experience – the bare basics of the mystical state that all people can aspire to attain i.e. a total perspective vortex – a contemplation of infinitude and complexity – which in the words of Ecclesiastes renders all rational explanations ‘hebhel’ meaning vanity – or more specifically absurdity.
So to answer the question yes the God-hypothesis for the non-mystic can be adhered to in the absence of the God-phenomena but only ever a fraction of the whole, an allusion to something greater – whether that be the miniscule self in the infinite whole, or a sense of order and meaning, or a sense of love, whatever…

The second question is controversial. My opinion would be that ritual and organised religion has a place in the sense of poetical theology. i.e. that a religion is a collective cast of dramatis personae acting out or re-enacting the mythic expression of social values and mystical nuanced sensations in a series of rituals much like a play.

Thats my anti-realist commentary.

I have two final points to consider.
Occams Razor for me is always a potential danger for over-simplification. Now as its supporters may argue if applied properly, sensibly and appropriately it is not an over-simplification at all. And the validity of the anti-razors must acknowledge that – in certain circumstances the Razor appears to be valid.
The question is – should it be a guiding principle of method?
My opinion is no it shouldnt, as constant conscious recourse to the razor raises the danger of a tendency towards over-simpliflying. Rather than a principle of method it should be viewed as a tool to be used in appropriate circumstances – where an over-complication renders understanding or knowledge incoherent.

My second point is back on the topic of theism. I am sympathetic to the Baudrillardian thesis that the image or simulation precedes reality.
I have my own formula of the idea (a complete description which I’ll save for another post) – I have a system of grades:
Pure idea (probably independent of human consciousness – which maybe infers an idea of a greater consciousness but that is merely an inference of perspective not an accurate observation) this can also be called ‘unthought thoughts’ or ‘logic’ – a priori ‘things’.
This followed by Symbolic Form – thought thoughts, ideas that we concsiously percieve and play with – the Symbolic Form finds its ultimate expression in stated ideas – words. I also call this Truth-Value.
Both of these grades are independent of external reality – things as they may seem to be/are which I also call Truth-Reality.
But:
Our descriptions and explanations and understanding of ‘Truth-Reality’ things as they may seem to be are constantly enshrined in our Truth-Values, or our symbolic forms.

Thus when I observe a ‘cube’ the ‘cube’ exists externally as a physical form – independent of its being percieved or thought about.
But it exists as itself, not as a ‘cube’.
A ‘cube’ is the thing of itself percieved and described as a ‘cube’. And the description or labelling of it as a ‘cube’ is the synthesis of the percieved Truth-Reality (the thing as it is) and the thought Truth-Value the symbolic form.
The thing as it is in itself, and the symbolic form of ‘cube’ that exists independent of reality, when combined with thought and perception presents us with ‘a cube’.

Applied to the question of scentific ‘proof’ and ‘disproof’ of God we must consider that the Symbolic-Form (the idea) of God precedes the reality that infers, proves, disproves, manifests the Real God.

Therefore in a very true sense of the word we define God into existence or non-existence.

But surely this is a contradiction? There cannot be a dual state of reality where God exists and does not exist at the same time surely?
Thus we return to the idea of absurdity and Wittgensteins admonitions that
“The world is the totality of facts, not things” and
“The limits of my language mean the limits of my world.”

Thus it would seem that in the case of a God that is supposed infinite, omnipotent and omniscient; the progression from pure idea (unthought thought), to Symbolic Form (thought thought) and External Reality is one that we cannot meaningfully express, perceive, or scientifically describe in its wholeness.
(Indeed if it were possible for a scientific work to describe, explain and prove God, then that book must be greater than God and thus what is described not be infinite, omnipotent and omniscient).

Thus the God of affirmation is elusive.
And all that is meaningfully said in Lennox’s book is “I believe in God”.

Where is God? I think the original greek of the introduction to Johns Gospel gets closest of all. In English “The Word” – in Greek “Logos” which is more than word, the “Logos” is beyond symbolic form – it is pure idea – unthought thought.

Perhaps a fraction of that unthought thought can be experienced i.e. finitude in infinitude.
But the unthought thought can never be adequately expressed in symbolic form.

So why does Lennox say I can prove scientifically and Dawkins the contrary?

Because in the existential world, our experience of the finite we have a natural urge towards creating a coherent and consistent synthesis of the symbolic form and the real world.

Ironically (and this is my final point – promise) the pure idea of unthought thought, and the pure-reality of the unpercieved object the thing as it is, exists wholly independent of the symbolic form (i.e. without our thinking it or seeking to bridge the two). This pure silent being of things as they are in thought and thing is perhaps the closest we can get to a meaningful inference of God – simple presence. And perhaps this is what the old design argument philosophers wanted but failed to meaningfully express, the inference of Gods existence by his unpercieved presence.