Pretty much everything Little_Jay said. I’ve played against a number of Laz players and it’s pretty frustrating when he, or another priority target, sits outside of the dome.
The short of it is that you have to just focus on someone else for a short time. Lazarus lacks some of the healing other medic’s bring to the field, so you can abuse someone who has no damage mitigation–for example, aim for the Support (avoid downing the Trapper, there are only a few of the Trapper’s that deserve to be focused over any given Support).
Something that I do is to simply go to the other side of the dome if there’s ample cover. That way if he wants to get in to help his team with any expediency he either will have to move all the way around the outside of the dome or go straight through it. The other part is that if you manage to sneak pounce someone if they come to you, or down them, camp the body. If you have feeding speed perks and kill them completely, you can do one of the best and trolliest things to a Lazarus player.
If you have a knock back or other zone control to keep the others off of you and there’s a dead body at your feet, you have a dliemma. Go after the others, and potentially let Laz get the rez? Or, camp the body to make sure Laz can’t res it, while trying to damage others. I like option three: Eat the fucker as soon as you manage to get a gap in people damaging you. It counts as two meats, so keep that in mind. Eating half of it won’t do the trick, you have to eat the whole thing. If you can manage that, then you’ll even have regained a little bit of armor, and the dome will go down soon, leaving you with the option of attack to try to drive the point home and stick on another tick, or run and likely have some free reign for a while.
Hope that helps!