Depends. I will only wear Lulus with pockets when I run because I run outside and I don't have an Apple Watch (I need Spotify and GPS for my watch so I bring my phone). The only compression running leggings they sell with pockets are Swift Speed and they discontinued the shorts. I do love the Swift Speed and honestly, I've bought a few pair of the shorts from Ebay. So my question here is do you want shorts or leggings? Do you require a pocket? I also only wear compression pants to run so the Speed Up line is out for me - Fast and free (they have them with or without pockets) is less compression which you may or may not like. Depending on your answers, I have a few more brands to suggest.
For weight training, the Swift Speed are too tight for squatting. I only have the Wunder Train and they are perfect. I bought the ones with no pocket so if you are at the gym it could be annoying to bring a phone, but they have a bunch with a pocket. I lift weights in my basement so it's not a problem.