Ok. Ya'll are getting that shit all messed up.
The photo is of Lydia. Lydia Crosswaithe. She's a friend of Thelma Lou's (and ol' Thel had some fucked up friends and family) that Barney tried to set Andy up with. This occurred because Andy was pissed that Nurse Peggy (Tatum O'Neal's mom in real life) had a jackass guy friend staying with her so Barney tried to fix things by getting Andy a different date. Lydia had the herpes.
Later in the series, Lydia was also used as a date for Goober. He was horning in on Andy and Barney's double dates with Bitch Crump and Thelma Lou and they encouraged him to act on his attraction to Lydia to get rid of him. No reference was made to the prior attempt to set her up with Andy.
FWIW, the same actress played Mayor Pike's daughter Josephine and also Mayor Pike's daughter Juanita in two other episodes (although we were never told if this was the same Juanita who worked at the diner).
The one you're thinking of ("she's a dog") is Thelma Lou's cousin Mary Grace. In that one, Bitch Helen and Thelma Lou won't go to some stupid ass dance unless they also get a date for cousin Mary Grace who's in town for some unknown reason. They coerce Gomer into it and he spends butt tons of money on clothes, socks, ties, and shoes with buckles on the side to get ready... only to run out of the room leaving a sad Mary Grace to mope alone. He later comes back because he "fergot her ker-sage" and they tear the living room up dancing -- meanwhile Bitch Helen and Thelma Lou drag Andy and Barney away from the dance because of poor sad Mary Grace all alone.
The woman who played Mary Grace also played the ambiguously lesbian carpenter on Green Acres. And her real name was Mary Grace.
She was not, however, a lesbian in real life. Married twice, the second time for more than 30 years. She birthed two children, none by Gomer or Goober.