Lakshmi is first mentioned in "The Guitarist Amplification" (S03E07) in the context of a date for Raj at his cousin Sanjay's wedding. She was going to specially fly in from London to meet him, but the plan did not go through.
In "The Transporter Malfunction" (S05E20), Lakshmi and Raj are considering an arranged-marriage together and on a date with Raj he learns that she is a lesbian and would marry Rajesh only to cover up that fact. She chooses him, as the rumor in India is that he is gay. Raj considers the option of marrying her, for the sake of getting his parents off his back. He ends up turning the idea down, wanting a woman who would truly love him.
- Lakshmi's last name is revealed in "The Guitarist Amplification", when Mrs. Koothrappali says via Skype "Sheldon, ask our son what we’re supposed to say to Mr. and Mrs. Choudry, whose daughter, Lakshmi is flying in from London, for the sole purpose of meeting him."
- Lakshmi on IMDb