Same(?)problem, but was able to improve
I had the same problem: After installing Lion, my Late 2008 MBP was unable to connect to equally old Airport Express base stations with a 300MBit link. My Airport Expresses are the older ones which are not capable of using 2,4GHz and 5GHz in parallel.
After Lion, not only was I unable to connect with more than 144Mbit, also the general transmit speed was a lot less than you'd expect=> From before 8MB/s (even with less than a 300Mbit link) to now around 3.5MB/s.
I also expected Airdrop to be part of the problem, as I was able to see with a scan that Airdrop sets up an independent 144Mbit always on network in the 5GHz band.
I went on to disable Airdrop (the whole service). Airdrop gone, but Airport Express still limited to 144MBit.
I have two Airport Xpress and a Fritzbox Router. Funny enough, the same MBP connects happily via 300Mbit/5GHz link to the Fritzbox, even post Lion. My standard setup, which worked great pre-Lion was to use the two Airport Xpress base stations to have 2,4GHz Wifi (between 144MBit and 300Mbit link) all over the house, and the Fritzbox to have a small 5GHz bubble (300MBit link, less crowded) around my office. As I mentioned, with Snow Leopard this would give me 8MB/s as a minimum all over the house in both bands.
It should be mentioned that even before, the only way to actually get 300Mbit out of the Airports was to change the country code to a few select countries, e.g. Ireland for 2.4GHz or e.g. Norway for 5GHz.
I used the Lion Wi-Fi Diagnostics tool to check out what was happening. The maximum transmit rate for the Airports (2.4GHz) was 130mbps, but the actual data speeds were much lower. Conversely, the average transmit rate of the Fritzbox (5GHz) from where I was testing was much lower (87mbps) and data rate was still over 8MB/s. I noticed that the country code shown was always AT, even though I had Ireland in the Airports. I reconfigured the country code in the Airports to CZ (update only possible if you change something), reconnected, Country Code shown was CZ, data rate went immediately up. But, after a while, the Country Code displayed changed to AT again - data rate dropped by 50%. The Fritzbox sends on channel 108 - that is not allowed in Austria (AT). This could explained why I would sometimes get a timeout when trying to switch networks. I have no clue who introduces the wrong country code (might be the Fritzbox, might be a neighbors network and it happens when scanning networks), but changing the country code of your computers airport card / base station drastically affects the wifi data rates possible with this type of Airport Express (Firmware 7.6.1), independently of the shown link speed - under Lion the MBPs airport card country code is collected automatically from the base station - at least in my case that leads to trouble. What I did is I moved the Airports SSID on top of the preferred connection list for the computers that typically have to go through the Airport network and deleted the unnecessary one. For now, this keeps the Country Code set to the one configured, which keeps my data rate high. Sounds like Voodoo, but works for me.
Update: It's the Lion Wifi Driver. It has bugs/problems (as of 10.7.3, at least with Broadcom chipsets). I downgraded to the 10.6.8 Snow Leopard driver. Kills Airdrop for good, but got rid of my general speed problems. Airport Express still only good for 144Mbit links though. I saved the IO80211family.kext from my Snow Leopard installation and installed in Lion with Kext Utility (just drag onto the window).
