You can but only carefully. Joke! Now seriously.
Thanks to modern technology, artificial lashes don't lose their original appearance even under the influence of high temperatures and UV rays. Glue also retains its properties. But because in the first 24 hours it is completely solidifying, it is worth abandoning the solarium, sauna, and bath.
Suncream causes more damage to the lashes because they often contain oil components. They, as you remember, affect very much the lash retention.
What is the result? Sunbathe, go to the tanning bed at least a day after the extension procedure, but don't apply oil-based protective products to the lashes and, of course, wash them daily.