I believe I have fixed the problem. (At least it worked for me). When I began to run a server on my computer, I began to use OpenJDK 7 instead of the Java SE 6 64 bit (Default) because it made it possible for me to run the server. That is when I started being unable to log into Tekkit, and just now, less than 5 minutes ago when I restored my default settings for the java, I was able to log in and play again. Just go to Applications, Utilities, and then click on Java Preferences, then drag the Java SE 6 64 bit back up to the top, or click Restore Default. Note: I am not a computer genius. This may have been just a coincidence, or dumb luck, or they have fixed it, but either way I just want to help, because Tekkit is awesome, and not being able to play it sucks. So I really hope this helped, and if it didn't then I'm sorry. Note: I have Snow Leopard, not Lion.
Edit: This Works!!!