My two cents:
There are many ways to improve your lifting and keep your hips healthy. Mobility work and recovery are prioritized in 5/3/1, so your hips should be just fine on this program.
I don't mean to be assuming, just wanting to cover all the bases, but if you are asking because there is a pre-existing injury, I would still avoid briefs. Buying them to feel better instantly would just cover up the injury, not treat it. You would have to address your muscular imbalance that causes it.
Final thoughts: Louie does a lot of box squats with an ultra-wide stance, which put a ton of pressure on the hips to do the work, but I am ultimately unfamiliar with his training philosophies outside of basic understanding.