Place a pillar over the lymantria, build a small shelter around it to keep it safe. Use a bola when it lands, shoot it with tranq arrows with a normal bow. Crossbow has higher chance to kill it. Feed it mejoberries.
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.
Don't attack it unless u have a plan a good one is to wait for it to land, throw a normal bola at it, then shoot tranq arrows at its head until it passes out, then feed it mejoberries or any type of berries, you may want to build a house around it to protect you and the lymantria from storms