Tamed Lymantrias make excellent base buddies. They are slow and agile - making them ideal for offloading dinos and building tall bases. They can also easily land on a target 1x1 square, and usually stay on that square if you need to turn while landed. This particularly is useful for reloading turrets or placing that last ceiling. For low level base buddies, level weight and stamina. For high level base buddies, only level weight.
A lymantria can fit through a single ceiling tile space but an argentavis can't. Build a trap with one ceiling missing in the corner. Use a lymantria to aggro an argentavis, fly into the trap and out the hole, leaving the argentavis in the trap. Easy argentavis tame.
I would highly recommend building some sort of trap when taming a high level. Otherwise, without a good tier weapon, even a bola won't prevent a high level from breaking free and flying off before you knocked it out! ~L
You're definitely going to want to use, bola, and tranq darts on this one. Too many arrows, will kill it outright(I'm not saying you can't use arrows. You have a high mortality rate if you put more than 3-4 arrows into it), very fragile tame. Bola it about a trikes length away from yourself initially... It's spore, is annoying to deal with.
Lymantrias typically are nonagressavive until attacked. Rather than a typical attack they use a large cloud of green acid that will temporarily slow your movement speed. The absolute best way of taming would be the bola method. To know our aim towards darts rather than the typical crossbow or stone and slingshot. Seeing as of these creatures have such low health. Happy taming!