Bonnie,
Mooscha would be a possible phonetic spelling of the name Moische, Moishe, Moshe, Moyshe, which is simply the Yiddish version of the Hebrew name Moses. The rendering of the vowel sounds of one language in another is always difficult, especially if the second language does not really have the sounds of the first language.
So it is neither Russian, nor Lithuanian.
The Hebrew text at top of the gravestone reads Mosheh Aryeh bar Tsvi which means Mosheh-Aryeh son of Tsvi.
Rabinowitsch is itself a Germanized version of the Russian patronymical surname Rabinovi(t)ch meaning 'son of Rubin'.
Do you have any idea whereabouts in Lithuania he came from?
Justin