sadly i don't know much about tamil fonts.
and i don't really know how to input tamil glyphs. but i'm confident that a current version of the development branch should manage it.
afaik scribus should work correctly with the abhaya libre font. i guess that we would know if they would not (iirc i easily got them to work with pathum four years ago...)
i have no idea if the un-abhaya fonts are also supposed to work, but i see no reason why they should not.
this having been said, a wild guess from my side: if you see english chars instead of the sinhala ones, it might simply be that you have not correctly configured the keyboard to use the sinhala mapping...
but it's just a guess, since i have no idea how your language can be typed on a keyboard (for my language we have a normal keyboard with a few additional chars here and there...)
but why can you type them in LO but not in scribus? no idea...
on top of downloading the fonts, did you do any configuration specific to sinhala on your ubuntu?