Looking for solution to keep LTM HA pairs syncronized across 2 data centers.

Dual data centre synchronisation is an operational support role. There are no tools for this. The closest you will get is writing tmsh scripts to build the virtuals, pools and servers then maintaining that script for each site. In theory you could write one script and substitute the relevant information. However there is no guarantee this wont disrupt existing operations. It becomes messy very quickly. This is a short example to change pools but its not very clean. The moment something does not match exactly it falls down like a house of cards.

for dc in d1 d2 d3 d4; do
  for vip in 1.1.1.1 2.2.2.2 3.3.3.3 4.4.4.4; do
    echo "modify /ltm virtual $vip pool newpool" >> run$dc
  done
done

for dc in d1 d2 d3 d4; do
  scp run$dc root@f5$dc:/root
  ssh root@f5$dc "tmsh < run$dc"
done