Which of Lily's attacks (melee or ranged) is more effective against Deathclaws?

Lilly absolutely svcks at ranged weapons. Give her a Chainsaw though, and she will make mincemeat of any Deathclaw one on one. Chainsaws ignore DT, and if the Fallout Wiki is to be believed, computer-controlled NPCs can deal catastrophic amounts of damage with them.

Plus, the CND of a weapon doesn't lower when wielded by the companion.

How do you get her to wield the Chainsaw? I put it in her inventory,what now?

Now she grabs it and cuts things up. Her default Vertibird Blade is much weaker than a Chainsaw, so there should be no problem. Don't forget to set her to melee.

I thought Lily couldn't use the chainsaw because she doesn't have any animations for it, just the two-handed swinging ones.

Set Lily to melee.

Not because it gives superior damage, but because that way she charges at them quick as hell and gets their attention. She's got the health to take their hits for a bit, so that gives you more time to shoot freely. Lily saved my ass from the Legendary Deathclaw that way.

You're correct. I have very little experience with Lilly. I usually just park her at the Lucky 38 as soon as her quest is completed.

That said, giving her Oh, Baby! is never a bad idea.

GRANDMA NEEDS A BIGGER PADDLE FOR THIS BEHIND!

God I love Lily. xD