Hello, You can tell Lyx to accept compound words:
when you start the speller, press "spellchecker options" at the bottom (right) of the window and then choose the radio button "Accept compound words". You can also reach this through Edit -> Preferences -> Lang Opts -> Spell checker. In both methods you can also choose the speller you use (aspell or ispell) I don't know the difference in behavior between aspell and ispell (after accepting compound words both gave me no errors for the sentence: "thespelling of eigenvalue"). I'm told aspell is better. you can ofcourse also tell the dictionarys to accept specific words, either in this session or to add them to your personal dictionary: press "Accept word in this session" or "Insert in personal dictionary" while runing a spell check. Hope this helps (sorry for any spelling mistakes - no speller in mozilla), Amir