Each arm has a Small Laser mounted that has not fired. 1st set of punches hits, both can execute a fist fire attack?
No. CO p75, "the Fist Fire warrior then fires one of the arm-mounted weapons," Only one weapon can be used in a fist fire attack.
Second set of punches from “Melee Master” hit. Can both execute another fist fire attack with the same lasers as the first? Assumption is no.
No. Fist Fire is a special maneuver that's not a physical attack, so Melee Master can't double it any more than anything else.
Note also that Fist Fire does not remove the restriction physical attacks have on not being able to physically attack if the 'mech fired weapons from that location already. So if a punch was delivered from the left arm, and fist fire used to fire a laser from the left arm, the left arm cannot be used for another punch from Melee Master since it has no fired a weapon.
And if the left arm laser was fired in the combat phase, no physical attacks can be made with the left arm, with or without fist fire.
There is no restriction mentioned on firing a weapon more than once because you shouldn't be able to trigger firing the weapon more than once with physical attacks. If it's fired a weapon from that location, no (more) physical attacks from that location.
What if the mech has a second set of lasers in each arm? Can those be utilized for a fist fire attack on the second melee master attack?
No. You can only use one weapon per Fist Fire attack, and you only get to use Fist Fire once/turn. (Unless we decide no on errata saying Fist Fire can only be used once per turn. Then you can use the other arm punch to fire one laser with Fist Fire for the first punch from that other arm. Melee Master could not be used to punch then, as both arms have fired weapons and can't be used for physical attacks.)
You cannot in general use fist fire with both punches: just 1 fist / turn.
