You need to be sure that (a) you are not firewalled in any way. Go to LW's menu bar, Tools -> Advanced Tools. It must not say anything about being firewalled.
(click to see larger view, shows difference between my mac & windows LPE)
(b) probably best if none of the options in the Performance window are disabled. ie: LW's menu bar, Tools -> Options -> Advanced -> Performance.
(c) becoming an ultrapeer might take some time. The longer your LW is connected, your chances increase.
LPE runs similarly to LW Pro. LPE might be lacking one or two things Pro has, though this would be in the internal code engine. When LPE was originally released, it was specified it was not Pro but built from the 'open source' LW Basic. It's based on the LW 5.6 Betas. Whether pro or basic, should still be able to become an ultrapeer regardless, if conditions are right.