I remember (watching the show in reruns as a kid) the robot as the B-9 Environmental Control Robot. On his packaging (a box or a metal cabinet, I think) you can see the name G.U.N.T.E.R., which is an acronym for General Utility Non-Theorizing Environmental Robot.
It should be your mantra whenever you apply products to the lawn. This doesn't have to be a lengthy ban. The Dog Owner's Guide suggests keeping pets off treated grass for 24 hours, as nitrogen can burn the pads of a dog's foot. The guide also recommends keeping pets indoors during application to prevent an airborne inhalation or skin contact.
Once it is neutered, still do not let it out of doors unleashed or unaccompanied. If you have a female dog or puppy, wait until 3-6 months after its first heat period to have it spayed. Time the surgery before its anticipated second heat period. If you have a female dog, let it pass through one heat cycle before considering having it spayed.