There are techniques to reconstruct missing pixels such as

Conference Paper Navier-Stokes, fluid dynamics, and image and video inpainting

Regards,

Joachim

you can use a timespan and then apply median function.

In this process you will get an average value of every pixel within that timespan.

but i am afraid that is it appropriate or not for LST calculation.

https://developers.google.com/earth-engine/tutorials/tutorial_api_05