"Ramen" and "going/went to get ramen" refers to cheating on someone when in a relationship. It's also used as a cover, either by the cheater or by the person being cheated on in order to save face.
(The popular ramen chain Ichiran can also be used as a synonym.)
"They're dating but he's getting ramen on the side."
"Tim didn't come home until 9 am the next morning? Even after all his friends turned in 6+ hours before? Where was he?"
"He went out to get Ichiran with our friend Paul (and didn't even bring me back any!!)."
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