I have heard that Gaudiyas believe that Krishna is eternally 15 years old and that Lalita is eternally 14 years old.
Why do they believe this? Is this stated in scripture?
Yes, it is confirmed by several gaudiya acharyas including Srila Jiva Goswami (one of the six goswami) in his tika of Śrīmad-Bhāgavatam. Srila Prabhupada discusses this in SB 10.45.3 https://vedabase.io/en/library/sb/10/45/3/