I found a post on the subject from the guy who wrote this book about Mac OS X internals. His post mentions Snow Leopard (10.6), but the issues would be similar for 10.7. See Mac OS X Internals - Is Your Machine Good Enough for Snow Leopard K64?
Here's the part I found most relevant to your question:
[...] Unfortunately, a 64-bit processor alone doesn’t suffice. Out of the
box, boot.efi will not boot K64 even if you have a 64-bit processor
and explicitly request K64 if at least one of the following is true.
- The machine has 32-bit EFI.
- The machine’s model is prohibited from booting K64 through a hardcoded list within the boot loader. (A cursory look suggests that
the list excludes "non-Pro" machines.)
Both of these "limitations" are technically artificial, albeit to
The first limitation actually does have merit and is arguably not all
that artificial. Although a 32-bit EFI could launch a 64-bit kernel,
the kernel, when running, would not be able to use firmware services. [emphasis mine]
In particular, you wouldn’t have NVRAM. For kernel developers merely
wanting to run a 64-bit kernel for testing and debugging, this may not
be an issue [...]
On the one hand, the author states that the limitations may be artificial, which still indicates some promise of a workaround, but on the other hand, as @Koen van Rhee's answer also already pointed out, you may end up with devices without support under 64-bit.
(Aside: Why do you want to run the 64-bit kernel, anyway? The OS X 32-bit kernel can run 64-bit programs.)
I did some more digging searching for a real workaround of some kind, not just theory. I found the following: OS X Daily - Got an Older Mac? MLPostFactor Installs OS X 10.8.3 on Old Unsupported Macs. OS X Daily's article links to a series of forum posts at MacRumors - [Guide] Success! Install 10.8 on old unsupported Mac. It is a very long thread.
I still don't definitively know if you can get the OS X 10.7 64-bit kernel running on your specific kind of Mac, but I suspect for the reasons mentioned in this image from the MacRumors forum thread that you can't: "Problem is cards like [...] Does NOT have 64-bit Kexts [...] 64-Bit Kernel will NOT load these 32-bit kexts". Essentially, what @Koen van Rhee already said.
But then I found this. Quoting: "Apple has included 64-bit drivers for GMA950 in the OS X 10.6.2 update. These drivers can be used to provide partial support for GMA950 under OS 10.8." ... and I'm thinking: maybe such kexts exist for your card and might work on 10.7 too, if they'd work on 10.6 & 10.8? You may have to hunt and mix & match bits from elsewhere.
To sum up: I don't believe there to be a single or simple workaround for your desired OS version and hardware version. If you want to proceed, everything I've read indicates it may be possible (to some degree — accept there may be missing drivers and so missing functionality and/or poor performance), but your work will be cut out for you.