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Lois is next to Clark on the bar and she's awfully
drunk. They're on her cousin' s engagement.

Lois: Another glass of bubbly? And throw in a Shirley temple for the lady.
By lady does she mean herself or she refers to Clark who never drinks?
Clark: Lois, don't you think you might
want to pace yourself?
Lois: Believe me, Smallville, I am
a lot more obnoxious sober, She's totally sober?

and the last thing anyone wants is me
making a scene at this blessed event. Chloe is barely legal, Just came of age?

and she is getting herself hitched to the first guy who's shown her any attention.
Present company excepted. She doesn't mind Clark being with her now?
Clark: Or you're just jealous of your cousin beating you to the altar?
Lois: This isn't a competition.
Clark: Then why are you keeping score? Meaning?
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As you probably know, a Shirley Temple is a non-alcoholic drink. I don't know who she is referring to. I don't know why she would call Clark a lady.

She means theat when she is sober she is even more obnoxious than when she is drunk.

Yes, "barely legal" means just old enough to marry.

"Present company excepted" means "except for you." Did Clark date Chloe earlier?

Why are you acting as though it's a competition if you say it is not.
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Hi.

Lois: Another glass of bubbly? And throw in a Shirley temple for the lady.

By lady does she mean herself or she refers to Clark who never drinks?
If there's no other woman present, I take this to mean that she's referring to herself in the third person. People do that occasionally, eg to be mildly funny.

Clive
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Comments  
Thanks, Barbara! That helped.
 Clive's reply was promoted to an answer.
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Thank you too, Clive!