For an easy tame, wait for the Lymantria to land and then place a tent directly where he/she is at. Its stuck until the tents durability dies out, this gives you enough to build a little house around it for a safe, easy tame.
With teamwork, it can be used to help tame other animals. One team member on Lymantria, the other ones shooting tranq. The slow effect is 90%, therefore, plenty to slow down any creature enough for a person to type it while shooting tranq shots.
Contrary to the dossier, a moth CAN be very fast. I had a moth with around 300% movement speed, which can outrun a wyvern. Unfortunately, due to no damaging attack, they can be hard to lvl, but and easy fix is to use a lystro. They are very good starter flying mounts.
The Lymantria is a moth-like creature that can expel a cloud of poisonous spores. While its slow flying speed make it a less suitable flying mount for transportation, survivors can use its spores to slow down enemies.