Do the alpha's that spawn in the lake legendary's caves respawn?

Question

On the page it doesn't say that their limited spawns also if they do respawn are the respawns shiny locked

Comments

In my experience, no.

Answer 1

Unique alpha Pokémon
These unique alpha Pokémon can only be found once during the storyline. With the exception of Vespiquen, they do not have the usual guarantee of any stats with individual values of 31 (starting effort levels of 3). The alpha Pokémon found in Acuity, Verity, and Valor Caverns are prevented from being Shiny, and have Scale values of 128 instead of 255.

The source states 6 Pokémon to be Unique Alphas, but only Zoroark (Acuity), Goodra (Verity), and Overqwil (Valor) as the Unique Alphas at the Lakes. These three cannot be found repeatedly, and they cannot be shiny as well.

Hope I helped!