You can create another club just for that tournament and make it private. That is what PNWCC did for some of their tournaments.
Custom Passwords in Live Tournaments and Matches

Creating a club tournament would have the same effect. I think lichess does the passwords because they don't have club.
The issue with passwords is someone could share it; whereas with clubs you as admin can approve them being in the club.

yeah, but there is already 432 players in my club. So will I kick out all of them?
No, you make a new club for the paid tournaments.

but, is this the only way? it would have been better if Chess.com enables the password option and live round robin tournaments

Creating a club tournament would have the same effect. I think lichess does the passwords because they don't have club.
The issue with passwords is someone could share it; whereas with clubs you as admin can approve them being in the club.
Lichess has clubs
Hello,
I am very active in Chess.com. Recently I went to lichess also. There, I saw something that is not in Chess.com. In lichess, you can make a password for any tournament and you can give the password to the members, who wants to play the tournament. Suppose, I am keeping a tournament with entry fees and prizes. So, I will only let the persons who payed the entry. But there is many members in the club by which I am making the tournament. Do I need to kick out all the players from the club who didn't payed he entry fees? This is very frustrating. I gained 400 members in my club and then I will have to kick out all the members just for making a prize money tournament.
So, this is my humble request to Chess.com to immediately make this option of keeping passwords in live tournaments and matches.