Hey OP, I am a Triathlon and Running coach. I think if this is a real goal of yours then you need to devote at least 2 days a week to running. Being that you are involved in a powerlifting program, I wouldn't suggest devoting a great deal of time to true speed work. Rather I would suggest, having one day devoted to a longer run (running longer than your goal of 2 miles while at a slower pace than your goal; start off modest, it can be as small as 2.2miles and slowly increase from there on a weekly basis) and another run that you can call a speed 'manipulation' of sorts.
Basically use that other run to do different runs where you challenge yourself by running in that 'uncomfortable' zone for a matter of time. Since your running has been limited and your goal is to run 2 miles in a certain amount of time, it can initially just be geared towards a time of say 20 minutes. this can be done in different types of tempo runs, but my favorite for lifters is 'Fartlek' runs which is where you jog easy for a set amount of time then run hard for a set amount of time, rinse & repeat for the entirety of the amount of time.
So if your fartlek run is supposed to be 20minutes, you can start off by doing 2min. easy jog followed by 1minute of as hard as you can, jog easy for 2 minutes, 1 minute hard as you can....etc. I like the fartlek for lifters because it is the closest to actual speed work, but leaves the body not nearly as beat up as after a true speed session. And you never stop running during the fartlek, which builds capacity at the same time.
And then you can change that up as you want to, so 2 minutes easy followed by 2 minutes hard, etc. This basically is the run day that will be teaching the body how to run at or faster than your goal pace.
Obviously this is just a bit of advice, and just like the lifting game, it is all about testing things out for you as an individual, see how your body responds and adjust from there, BUT you should ABSOLUTELY be able to hit your goals. Sorry for the scattered-ness of the post and I hope at least some of this made sense, as i was writing it in a bit of a rush!