If the child requires a seat, then he will sleep very well, with 1 pillow/blanket under him, to give him more flat surface.
If the child does not require a seat but is close to 2yrs, it will not be great, but OK. He will have to sleep in his mother's arms, making it comfortable for him, but not easy for the mother. The seat is wide, but the armrest is not adjustable, so you are pretty much stuck in your seat.
I would just take the TK flight, as you avoid changing in LHR and an extra leg. The cabin will be dark 90% of the flight time, so this should keep him sleepy and less active. If you change in LHR, the second flight will give you an active 2yrs old baby on-board, and you will still be tired from the first flight
