I will take recs on another studio album, however.
I wouldn't go backwards. Nightlife, which precedes Fighting and also has Brian Robertson on guitar isn't great IMO, and the three before that one with Eric Bell are pretty sketchy.
Black Rose comes after Bad Reputation and has the great Gary Moore replacing Robertson. It's a decent, if uneven album, but it does contain the amazing title track and Waiting For An Alibi and Got To Give It Up...all three are essential tracks for me.
The next two, Chinatown and Renegade have Pink Floyd 5th member Snowy White taking over for Moore. To me, this is a real sweet spot. Renegade is my all time favorite Thin Lizzy album, and probably a Top 25 all timer for me. If you like Killer Without A Cause, you'd probably like Chinatown a lot.
Their final album, 1982's Thunder And Lightning has John Sykes replacing White. Generally it's a more hard rocking album, but it's filled with all kinds of great songs.
To me, I'd just go chronological.