The best place to find a Kuva Larvling in Warframe is on Cassini, Saturn. Since it demands the minimum level requirement, and it's a Capture mission, you can use Cassini, Saturn to complete your mission very quickly if you have a good arsenal.

How do you get KUVA Lich to spawn?

Kuva Larvlings will only spawn after you have completed the The War Within Quest. After the screen flashes in any level 20+ Grineer mission, players are required to kill at least 10 enemies in under 1 minute for the Kuva Larvling to spawn.

How do I spawn my Lich?

Once the larvling has been slain, your lich will rise.

From the corpse of your baby Grineer a lich will rise: a (mostly) randomly generated nemesis with warframe abilities who will invade nodes throughout the system. You can only have one active at a time, and you must take down the current one to spawn another.