Sure, lie flats are 'nice', but not in this situation.
We took our daughter @ 18 months to CA, in DL F, and used this thing:
I don't know if a car seat is allowed in general but its almost certainly not allowed on the lie flats...
We also recently flew the AC pods from YYZ-SFO in her own pod, but it was easier to manage her when we were just 3-across in Y.