What is the correct pronoun in 'Lorna and me I entered the room'?

The correct pronoun would be "I": Lorna and I entered the room.

To make this clearer, you would say "I entered the room." rather than "Me entered the room".

The pronoun "I" is a subject pronoun. The subject of the sentence is "Lorna and I", a compound subject.

The pronoun "me" is an object pronoun, a Word used as the object of a verb or a preposition.

Example: The door opened for Lorna and me. (the compound object of the preposition 'for')