15 years old - congratulations on being such a good axolotl keeper! I aspire to match your success someday.
I haven't heard of them mourning like that. The theory is, they are asocial and don't really care if there are other axolotls around. However some, people have reported that their axolotls seem to miss a lost/removed companion or if separated by a divider, to hang around near each other on either side of the divider. I guess their axolotls didn't read the theory books. (I have not observed this sort of behavior myself.)
There is another possibility - could your axolotl be sick? I know your other was very old , but perhaps it had also gotten ill? Keep a close eye on your remaining one and see if any symptoms develop.