Shaun, I bought my (very expensive) MBP earlier this year to escape the constant frustration of trying to work with PCs/Microsoft - so I'm a MacBook novice!
The MacBook came equipped with Snow Leopard and worked faultlessly - I was delighted with both performance and user-friendliness.
Given Apple's great reputation for quality, I installed Lion without hesitation as soon as it became available. Perhaps naively, I never expected Microsoft-style problems in an Apple software release!
You won't be surprised to learn that I now have exactly the same problem with wi-fi connectivity as yourself - when waking from sleep mode Safari reports 'You are not connected to the Internet', even though the Wi-Fi indicator shows 'Wi-Fi: ON'. (This is constantly alternating with 'Looking for Networks...').
When I run diagnostics the system reports the internet connection is good.
If I then close & relaunch Safari, it comes back OK.
I NEVER HAD A WI-FI CONNECTIVITY PROBLEM WITH THE PREVIOUS SOFTWARE.
I have communicated twice with the support people at Apple and both times they had me alter various settings in system prefs - all to no avail.
So, deeply disappointed that I spent all that money and seem to have a flawed product and a useless support service; eagerly awaiting the fix....