240 sortie rate for ford is for short periods only, a surge period of a day or two. its goal for a more sustainable sortie rate is 160 sorties a day. Nimitz's limit is 200 for surge, 125 for prolongued operations.
Actual wartime operations over several weeks time ALWAYS offer even smaller sortie rates than that.
They basically tend to drop towards a single sortie per aircraft per day, in normal conditions - no excess pilots, realistic distances crossed to target, maintenance needs etc.
Land based planes have always had a little better sortie rates than carrier planes, but they too, as history teaches us, don't do much better over longer air campaigns. In the last 4 air campaigns US took part, 2 of them were around 1 sortie per plane per day (serbia, iraq 2003), one (Libya) was even under 1 sortie and one (first gulf war) barely made it to 2 sorties.
Also, for a decade now, standard usn combat air wing trained with a structure of four squadrons, each having no more than 14 planes, often 12, sometimes just 10. 48-52-56 combat planes is a realistic number for Ford carriers in the future. Of course, those 160/240 sorties also count in growlers and hawkeyes. While theoretically Ford could do 4 sorties per plane for a day or three (as shown in one staged exercise at the above link), a more realistic maximum limit is 2.5 sorties per plane. Even that won't be sustainable over a period of several weeks. granted, not many operations may need such long commitments from a carrier force. Judging by history, after 2-3 weeks that should fall under 2 sorties per plane per day and keep dropping towards a single sortie per plane per day for campaigns that last more than two-three months.
Limiting factor for nimitz, ford or liaoning isn't the deck, catapults, ski ramp or arrestor system. Real limiting factor are air crews, their number and the fact combat missions are quite tiring. Ground crews suffer from the same limit, once we're talking about day after day after day operations. Then, after several days of hard hitting tempo, maintenance becomes a factor too. few hours of maintenance per plane stops being enough and overnight maintenance needs to be performed.
Basically, limit is crew numbers and available space for all any additional crew. Unless Liaoning has a worse ratio of air crews/ground crews per plane than Nimitz, it won't have much worse sortie generation rate either. A fairly small force of 24 J15 planes should be, in my opinion, quite decently served by Liaoning's crews and achieve similar sortie rates.