Just reviewed LBB8, doesn't have a specific ruling in the robot combat section, which is more about speed/stats, damage determination and repair.
But there is a subtle bit that does determine how many weapons can be engaged at once.
The weapons skill rule stats that there must be one application running per weapon- note that is not weapon TYPE, but just weapon.
So if a robot has 4 snub pistols, to fire all four at the same time it would need to be running 4 Snub Pistol-1 programs at once.
That puts the effective weapons at a time squarely on the CPU limits, plus whether a designer considers 1 Snub Pistol-4 or 4 Snub Pistol-1s to be more effective for the robot's mission.
Keep in mind those weapon programs could reside in storage most of the time, so the robot could be cargo handling, patrolling, autostewarding or surveying, and the need arises, in switches the weapons program and out pop the weapons.