Don't think it should be his father's responsibility.
It's important the club and de la Fuente have good communication so that they can put up a plan on how to keep Lamine as helpful as possible for both club and NT. Schedule is packed ahead with another international break coming up. Ideally Lamine would be kept out and rested during that but we all know he'll play at least 120 minutes over two games.
Of course Flick is going to have to rotate more from now on. Ferran, Ansu, Lewy, Raphinha, Yamal and Victor should be enough for the three front spots.
And keep his head cool too. I know it's fun to play in Barcelona while being 5-0 up in the 60th minute, but sometimes it's for the better to be subbed than to try to statpad for half an hour. Being 17 can be hard to understand that.