Miss Lonsdale is a side character who plays only in two episodes of the Queen’s Gambit. She doesn’t have any involvement with the adult Beth.
She’s a chapel leader at the orphanage where Beth grew up after the death of her mother. She’s shown educating Beth in the 2 episodes she’s in.
Rebecca Root plays Miss Lonsdale in this TV series. She represents exactly what Miss Lonsdale should be in the story of Beth.