Yes, there needs to be a double axel by itself in the long program.
I remember last year, Mirai fell down on a planned combination or something. Then, in panic, she started adding double toe jumps to everything. She even tacked on a double toe to a double axel. This of course, broke the rule, and the combination didn't count. If she had only done a single double axel, she would've gotten a bronze at Cup of China.
Mirai got the 2A-2T discounted because she did a 3Lz combo, a 3Lo combo, and did two 3F without a combo, so got a +SEQ mark. The SEQ mark counts as a combination, so when she did 2A-2T, that counted as her 4th combination and it was voided.
LP requirement is only an "Axel type jump" must be included somewhere. It can be a single or higher and 1 ft axel if you can...
burnt is right.