As I mentioned a couple weeks ago, Lithuanian is one of the most conservative languages in that it has retained archaic features of older Indo-European languages. One example of this is the word for grandfather, senelis, which comes from their word senis, meaning an old man. If the Lithuanian words bring the word senile to mind, there is a good reason for that. Senis is a cognate with the Latin senex, which is the word that also became the basis for senate and senator.
Senis is believed to derive from the Proto-Indo-European senos, which has other offshoots in different branches of the language family. Celtic languages have their own versions of this with sean in the Goidelic (Q-Celtic) group and hen in the Brythonic (P-Celtic) group. You can compare the Irish word for grandfather (seanathair) and the Scottish Gaelic word (seanair) with senelis to see the link between them.
It is the Brythonic word hen that was used to first describe Old King Cole as Coel Hen, whose legend was based on a real early medieval king in what the Welsh poets came to call Yr Hen Ogledd, the Old North. Today it is used in the modern Welsh national anthem, Hen Wlad Fy Nhadau (Old Land of My Fathers). The words for old or old man in a number of Indo-European languages are quite ancient, and in some cases they have not changed very much at all.
It would hardly be fitting to have a new word for "old." Although we do have "dotard," "codger," and "crone." Those are probably old as well, I suspect.