This. And there are plenty of super-lean unconditioned people. I run a climbing gym. I see them all the time. My guess is you can keep lifting heavy and just add some conditioning, maybe one session of intervals per week and two longer zone 2 sessions. Here’s more on zone 2 work.
Or just add finishers to the end of your strength workouts. There’s a lot you can do to be better-conditioned. Of course, if you specifically want to lose fat (hard to tell from your post if you wanted to be less fat and/or just be in better shape) that’ll come down to diet, and I won’t comment on that because I don’t know anything about it.