After installing LyX in Ubuntu 11.10, the functionality of the spell checker on-the-fly is not activated yet. To enable the spellchecker active while you are writing and giving you underline word if it misspelled, you need the following settings:
a) From the menu Tools > Preferences
b) Under the Language Settings > Spellchecker
b) Enable Spellcheck continuously and select the spellchecker engine Enchant
c) Apply and save the changes to close the dialog. Now spellchecker is already active continuously.