NBA rules prohibit a team from trading their #1 pick in consecutive drafts. This comes from a rule in the 1980's (the Stepien rule). The rule was created because Ted Stepien's Cavs traded away five consecutive #1 picks. Those picks ended up being the following players:
1. Al Wood - 1981 #4 overall
2. James Worthy -1982 #1 overall
3. Rodney McCray - 1983 #3 overall
4. Sam Perkins - 1984 #4 overall
5. Detlef Schrempf - 1985 #8 overall
That is a pretty solid group of picks, including a Hall of Famer and two other guys that had nice, long careers.
As for what the Lakers can do with their cap space, if they are smart, rather than trying to land a max guy, they should try to get two solid players. JJ Redick or Danny Green would be a nice addition on the wing as a shooter. A two way guy like Malcolm Brogdon that can play either guard spot would be a good fit.
With New Orleans, they are in a great position. They get Zion and a nice group of young players from the Lakers. They were able to keep their roster intact and they have the #4 pick this year, plus extra first rounders in 2021 and 2023. If they are knocking on the door in 2021 or 2022 they can move an extra pick to round out the roster then. They could also shop the #4 this year for something in the future, or for more immediate help, although if it were me, I would keep the #4 this year to give myself another good young player (Coby White from UNC could be an enticing pick).
The Lakers got the best current player, but New Orleans got so much back that it may not hurt them long term.