I've started playing Lonesome Road, and during the second talk with Ulysses, he talked to me as if I supported Mr. House. The thing is that in the long run, I don't want to support him I just stopped doing the main quests at some point and started doing the DLCs. So I wonder if some things in lonesome road, are dependant on what faction you choose or if Ulysses was going to talk to me about House anyway in that moment?

The faction-setting in LR is kinda weird, I suppose you have a good Strip-rep? So he thinks you're House.
There is a good mod for it if you are playing on PC which determined this based on where you are in the main quest, but I'm not sure if it works if you already started LR.

Yes, I do have a good strip reputation. I want to help out House for now but in the end I want to help Vegas gain Independence.