I just installed Debian Lenny with LXDE on a Dell Inspiron 8600. Iceweasel is now default in LXDE, but there seems to be some kind of permission problem. I was not able to start Iceweasel as a normal user – It only ran as root!
The problem was that ~/.mozilla did not belong to the user, but rather to root! So I changed ownership, and everything worked just fine!
sudo chown <myusername>:<mygroup> .mozilla