LHDs have long enough decks to launch both UAVs and STOVL aircraft like the HArrier or F-35B.
The Wasp Class, the America class, and others will all launch them without the need for a catapult. (Cavour, Juan Carlos, Canberras, perhaps the 22DDH for the Japanese), now, some of these also have ski jumps to help, but the Wasp and America class will be very adept lining up aircraft on the aft 2/3rds pof the vessel and launching them relatively quickly if necessary one after the other. Then, when they land, they do so vertically.
So, as a result, I do not believe we will see any catapults on the PLAN LHA/D. They are simply an added extravagence for those types of vessels that are very costly and take up valuable space for the machinery.
A good LHA/D can serve adequately as a Sea Control carrier if necessary with numerous STOVL fighters. They also serve very strongly in the air assault and (if they have a well deck) the amphibious assault role.
If you need the truly heavy sortie rates that catapults can bring to the party, you will bring in your large aricraft carriers for that.