What is a Lamia’s plane of existence if the original mortal was a Fey Eladrin elf and the Lamia lives in the material Plane?   Is it the Abyss, Feywild, or Material plane?  I suggest Abyss because the demon Lord Graz’zt creates them and they speak abyssal, but it seems like they live on the material plane.  

Yuan-Ti

How old to Lamias live to be?

If they have lion characteristics is it not possible they can do leap attacks to knock an opponent prone for a raking attack?

Any thoughts about bird or snake versions?

Serpent version: https://en.wikipedia.org/wiki/Lamia 

Mesopotamian version: Lamashtu is depicted as a mythological hybrid, with a hairy body, a lioness' head with donkey's teeth and ears, long fingers and fingernails, and the feet of a bird with sharp talons. She is often shown standing or kneeling on a donkey, nursing a pig and a dog, and holding snakes. She thus bears some functions and resemblance to the demon Lilith in Jewish mythology.

Medusa was a Gorgon in Greek Mythology Gorgons tend to be portrayed somewhat similar to harpies but their arms are independent of their wings, they also do tend to be depicted as scaly and I believe all gorgons have snake heads rather than hair, Medusa had more Lamia like features as a result of the curse Athena bestowed upon her, removing her wings, replacing her legs with a serpentine tail, and making it so whenever a mortal looked her in the eye they turned to stone. But yeah Lamia were essentially the Greek version of a Naga with one large difference being the Lamia were child murdering monsters while the Naga were strong, powerful, and dangerous beings that tended to help mortals

Medusa being cursed by Athena is actually a Roman myth, not a Greek one. Medusa in Greek myths was like other gorgons, though one of the oldest depictions we have of her actually show her has a centaur, which makes the fact that she is the mother of Pegasus suddenly make a lot more sense.

I also believe Lamia had varying descriptions, and being half snake was just the one of them. I think it was a poem from the renaissance that made everyone start to depict her as half snake.

So many monsters share this name and none of them that i know of have the lower half of a lion. This has pained me for 30 years

What's the point of giving lamias the ability to Disguise Self but only to a humanoid form?  They're still Large creatures so they'll be noticeably bigger than any humanoid should be.  The most they can do with their hindquarters is hide it as something other than their body or make it see-though and hope no one walks up behind them.  They can't disguise themselves as a centaur because centaurs are considered fey. 

Can anyone give me help? I’m trying to make a desert DnD campaign with a powerful arch lamia at the center of it, What abilities should I give her?

Quote from PollyNim >>

What's the point of giving lamias the ability to Disguise Self but only to a humanoid form?  They're still Large creatures so they'll be noticeably bigger than any humanoid should be.  The most they can do with their hindquarters is hide it as something other than their body or make it see-though and hope no one walks up behind them.  They can't disguise themselves as a centaur because centaurs are considered fey. 

 I think it might mean a creature that looks humanoid. Or it could be used to make the lamia appear as a larger, more powerful enemy for the party to waste their good spells on.

would

yes but i think they didn't want the Yuan-Ti and Lamia's to be mixed up

Late reply, but you can blame that Gygax guy for the lion part of the lamia. (:

If you dig out a copy of the 1e AD&D Monster Manual, yep, the lamia is half-lion.

Might as well add that, if you really want to adhere to Greek mythology, the lamia (and gorgon) are unique creatures. There's only one of them each in existence.

Would be amusing to have an adventure where the players are caught between the naga half-snake, and the lamia half-snake! (:

ENWorld has more info: https://www.enworld.org/threads/the-secret-historie-of-the-gorgon-lamia-and-su-monster.667485/

Hey I know this is super late but the reason is lamia are denizons of grazzts the demon lord's plane they act like succubus and try to woo travelers and then they hit them woth the intoxicating touch. 

The D&D Lamia comes from Edward Topsell's History of Four-footed Beasts (1607) (which appears to be somewhat based on hyenas).  Gygax may have been more familiar with Topsell's bestiary than the deep cuts of Greek myth.  However, the snake-like Lamia has been published as "Noble Lamia" in 2E.

disguise self (any humanoid form)

how do folks think  this works,  disguise self  as written means you can’t shift more than 1ft in height and have to have the same configuration of limbs.   I assume the  limbs configuration is ignored by the  ‘any humanoid form’ caveat.  is the height restriction also ignored?   Given that for example a  gnome is a humanoid form and a 9ft gnome doesn’t make a lot of sense.