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"?
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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.