My suggestions/comments:
1. If you are using Asia Miles, try to get her a J award at the airport counter with additional miles. Then all of you can be in J and can have lounge access.
2. I don't think the check-in agent can issue an additional lounge invitation. Even for MPC members, guests will not get separate lounge invitations. However, you can check at the lounge to see if the lounge agents allow her to enter. With the other passengers on J, they may - situation dependent.
3. If you are a MPC member, you can burn 7000 miles for a lounge invitation, but I don't think it is worthwhile. It is easy to spend time in the Hong Kong Airport. You do not need to waste your miles on a lounge invitation.
4. When boarding, you can tell the FAs that you are swapping with your grandmother. You should stay in Y. Visiting the J cabin by Y passengers is discouraged (in fact prohibited).