Is it possible to list all LTM pools load balancing method?

If you need to get the

tmsh list pool load-balancing-mode

output from multiple hosts in one shot, you can use iControl REST. The following bash script gets the load-balancing-mode information from two hosts: 172.16.1.133 and 172.16.1.155. Assumed that the admin password was common for both boxes: i.e.,

for i in 133 155; do
  echo -n $i
  curl -sku admin: https://172.16.1.$i/mgmt/tm/ltm/pool?\$select=loadBalancingMode \| 
  python -m json.tool | fgrep '"loadBalancingMode"'
done

For more information on iControl REST, visit iControl REST Home.