It is not currently possibly to use a LOVEtheatre voucher on ATGtickets.com The vouchers are not interchangeable and must be used on the corresponding websites.
For West End Shows, ATG vouchers can be used to purchase tickets for The Ambassadors, Apollo Victoria, Duke of York's, Fortune, Harold Pinter, Lyceum, Phoenix, Piccadilly, Playhouse (Kit Kat Club), and Savoy theatres.
Any other West End venues listed at ATGtickets.com only accept LOVEtheatre vouchers.