The Los Angeles Lakers can theoretically have max cap space, but only if Anthony Davis leaves as a free agent. In any real-world scenario they will have room for the full MLE, and should have enough wiggle room beyond that to keep Caldwell-Pope if the number is reasonable.
Doing both those things could push them a few million into the tax. I have them with just under $22M to do both and stay below the hard cap, presuming the team waives Quin Cook’s $1M guarantee and stretches it. That implies about $12M left for Caldwell-Pope, although they would gain more wiggle room if one of Avery Bradley, JaVale McGee or Rajon Rondo opts out of their 2020-21 contracts. None seem likely but all are at least somewhat possible.