Can Kindred use Lamb's Respite on the enemy's fountain to grant her teammates immunity from the Nexus Obelisk's laser?
No it does not. During Lamb's Respite you are still targetable and as long as the nexus laser can target you it will deal damage.
A zhonya's or fizz's trollpole allows you to jump in the fountain and survive due to the laser unable to target you. But Kayle's ultimate won't save you as you can still be targeted and take damage even though no other source can damage you.
EDIT: Dying in the fountain will not trigger gaurdian angel and Zilean's ultimate. Passives like Aatrox's or Zac's don't trigger either. Tryndamere's ult does not work even though he shouldn't fall below 1 health.
The passives from Kog'Maw, Sion and Karthus do trigger because they do not prevent death. Sion will still be targeted by the fountain after he died. I am not sure about Yorick's ultimate. It does revive a player but will not prevent death or grant immunity to damage.