What is the Sixth Step of MacBook Repair?
Solution 1:
Take it to Apple and ask them to fix it under warranty. If you have made a clean install, and can still demonstrate the problem, you almost certainly have some sort of hardware issue.
If you did a reinstall, then added something that has a kext, that might be responsible, though, so in the (unlikely) event, reinstall, don't install that, and see if that fixes the problem.
Solution 2:
@bmike's suggestion is written as a comment, but in fact it's a good answer: do you have an external bootable drive that you can use for troubleshooting? That will at least let you determine if your internal drive is the problem.
Prior to upgrading to Lion I had a strange, intermittent issue with my MacBook Pro logic board. It wasn't a big problem, but became even stranger and much worse after upgrading. I had it swapped out under warranty, but perhaps it's some anecdotal evidence that installing Lion may bring to light pre-existing hardware issues that weren't obvious before. RAM issues crop up frequently in the category of surprising Lion-related problems.
But if you are correct in thinking that you had no hardware problems before installing Lion, it's still more likely to be a software issue. In principle the next step should be reformatting the drive, and doing a true clean install of Lion -- meaning manually migrating your data, rather than using the Migration Assistant.