A player that has a LNTC has the same list. However, once he is traded, a new team does replace the team he was traded to.
However, for a player with a full NTC/NMC (like Nelson) who provides a 3 team list, they must remain with the club they have been traded to for one calendar year. So, in this case, Brock cannot he traded until July 10th, 2020. At which point, you will be provided with a 3 team list.