I could've sworn there WAS some movement for "justice" (i.e., war) in the wake of the Lusitania, IOTL...
Maybe a little in the northeast. But straight after the sinking, Congressional leaders came to Wilson to caution him (probably needlessly) that a war resolution wouldn't fly. Of course the TTL Congress might be Republican, but even if it were (not certain if TR's election was close), there was just as much opposition to war among Republicans as among Democrats - possibly more. If he talked war he'd be told to cool it.
You do know that TR and Cabot Lodge were really close, in real life, right?
Perfectly - and if anything Lodge was even more bellicose than TR - but in 1915 even he was cautious in his choice of words. He knew it was too soon.