What are your goals in the next six to nine months? Where are your lifts right now? If you are still in the midst of getting stronger rapidly, I would not interfere with that. If you are putting on fat too rapidly, just dial back the food intake a touch and see what happens. The recommendations below may not apply to you, especially if you are still in the midst of an LP. They are intended for peeps that are in intermediate territory.
Dietary intervention is necessary if you wish to get leaner, but some additional activity can chew up some calories, too. I like running with prowler with a weight that is heavy enough to provide resistance, but not so much that you start to grind at the end. You probably don't need to start with 6 trips of that at the start, however, unless you are already in pretty good shape. Four is probably a good place to start for your first prowler workout. If you push things too hard on the prowler at first, you will probably end up regretting it. That thing sneaks up on you. You don't realize what you have done until after you stop.
For running, I like 400 m sprints, but they will make you sore at first. I would start with three or four 400s with rest as needed. Worry about limiting rest after you get accustomed to the conditioning and don't try and redline things on your first workout, or two. Just like with lifting, start out conservatively.
You can also do stuff like walk for 20 or 30 minutes each day, or start riding your bike to work, or on errands. All this seemingly low effort stuff ups caloric demand and does it in a way that, over the course of a few weeks, can be useful and won't interfere with lifting.
Here would be my top suggestions:
Walk or ride your bike more just in the course of your day.
Prowlers
Higher intensity stuff on the stationary or real bike. Finding a hill to pedal up really hard for 20 sec on, 1:40 off is a good, very low impact way to get a conditioning stimulus. Probably don't need a lot of these to start, either.
Rowing is good, too. 20 sec on 1:40 off works, as does rowing a 2K. It requires a touch of technique and can bother some people's backs, but, as with all of these recommendations, it is low impact and has little eccentric work to make you sore.
Thereafter, running 400s would be my go-to, but realize that doing so will make you sore at first. I used to be a runner, so I have a soft spot for that. At the end of the day, any of the conditioning stuff can be sifted in provided it is done so thoughtfully. The first choices are the things that don't make you sore. I would rate jump rope and long, slow distance runs at the bottom of the pack.