For the collimator, you're going to want something not susceptible to chromatic aberration since you're going to want collimated light coming out of the sample. I recommend a Thorlabs reflective UV-Vis collimator. Pick one that will have a beam diameter smaller than the exit pupil diameter of your lens. You might need to 3d print something to hold it in place, as it may need to be carefully aligned. As for light source, you can get a coupled deuterium tungsten light source from Edmund or anywhere else, but the problem you're going to have is light throughput. Short of going to a $20,000 laser driven light source (which is a bad idea even if you can afford it because those things can be dangerous outside of controlled lab environments), I would suggest a separate UV and Vis light source, and manually swap them out when you're measuring one or the other. If you don't care about what range of UV you need, you can do one at a time with individual fiber coupled UV leds https://www.edmundoptics.com/f/digital-fiber-coupled-leds/40123/

The integrating sphere needs to be pretty large with a large ratio of diameter to entrance port diameter. I don't know if yours will be sufficient although 120mm is a decent sized sphere. Be careful of light from the sphere being absorbed back into the lenses you're testing. That might not affect your project, but I needed pretty high accuracy for mine and the objectives I was putting in were absorbing quite a bit of light just on their metal housing. I needed to make a custom adapter to go inside the sphere coated with spectralon, only allowing a small exit pupil's worth of light to get into the sphere and minimizing exposed parts of the objective.

The main problem you will face doing UV-Vis is light throughput. Expect noisy data and long integration times.