: I don't know if he would have cared much about Tycho's fate
: if it weren't for Tycho's odd and antagonistic fixation with Durandal.
Tycho and Durandal are competing to avoid the end of the universe, as Tycho says in "Welcome to the Revolution." (As Marathoner325 pointed out earlier, this is probably due to Tycho picking up some of Durandal's personality when he was rebuilt.)
I too foresee the imminent collapse, and know that we have both begun to realize how it may be cheated (though the price may number in the tens of thousands of stars). May the best sentience win.
Tycho and Durandal are probably keeping an eye on each other in case either discovers a new clue. Leela probably doesn't share the impulse, if she's satisfied with her planetary network instead of scouting around in a ship. For the purposes of their shared obsession, then, Leela is irrelevant until they need her help. Bigger fish to fry!