Run LyX and press Ctrl-N to open a new document. Write a few words in English, and press Ctrl-D. Yap, MiKTeX's DVI-preview program should be opened; check that it displays the text correctly.
Open another document and call the menu Document → Settings. Select there in the Languages section Lithuanian, press OK and type in a few words. Press Ctrl-D and check the output.
In the document settings you must use the Language Default encoding (which is Baltic (ISO 8859-13)). The other offered Baltic encodings are overwritten by the littex package.