Replace the life system with a "Death Counter"
I made a thread awhile ago asking what's zombie massacres identity. Asking if ZM's focus should be survival or a competition. I plan on posting more suggestions related to this discussion.
To get back to the point, players will be mainly fighting for kills to maximize points for upgrades and units. So hypothetically speaking there could be a situation where you're dead and out of lives and the only way to get back into the game is for someone to revive you. However your teammate(s) refuse to revive you because you'll take away from possible kills, which means more points and units for them.
Instead of having a certain amount of lives, how about instead have a death counter that will increase your respawn time each time you die. It's a slight edit but I feel like that could solve this specific hypothetical situation.