Is it correct to say
"My daughter will be waiting me on the Dulles Airport lobby"
"My daughter will be waiting for me on the Dulles Airport lobby"?
It is "waiting for me."
*Waiting me" is not standard English.
Also, the preposition on is not correct here. It should be in or at.
It's wait for X, not *wait X.
The verb wait is usually intransitive, so it doesn't take a direct object:
*My daughter will be waiting me in the Dulles Airport lobby.
This is ungrammatical. Me is a direct object, but wait doesn't take one.
My daughter will be waiting for me in the Dulles Airport lobby.
This is grammatical. Wait takes the preposition phrase for me as a complement.
The use of wait as a transitive verb is fairly limited:
In our senior year Jack took a part-time job waiting tables in the Violet Cafe.
This is a fixed expression meaning something like "working as a waiter in a restaurant; working at a restaurant, serving customers at tables".
Get in line and wait your turn like everyone else.
This is a fixed expression meaning something like "wait your turn; wait until it is your turn to do something".
Outside of fixed expressions like these, wait is typically intransitive.
In this answer, the * symbol marks a phrase or sentence as ungrammatical.