You also need to know your city rules/laws. We typically use same or similar verbiage as the rec centers and public pools.
Years ago NAAs suggestion was those under age 14 should be accompanied by an adult when using pool/equipment that might be unsafe.
It sounds good to say lease holders only but how many children are lease holders? I doubt that would stand up in court. Plus people whose first language is not English might not understand the verbiage.
Check your gym equipment documents and see if there language regarding age and safety.
Always good to ask local FH folks/attorney.

I am posting on my pool that all occupants and guests must be accompanied by the leaseholder.

We just had a violation from HUD and had to change all of our common area signage and rules to read things like “persons under the age of xx should be accompanied by an adult”. We use the recommended age based on the local ordinances set by the city of health department as a guideline and we were required to take out words like “MUST be accompanied by an adult” and changed to “should” or “it is recommended.” It cost a small fortune to change all of our signs at all of our sites.
GOOD LUCK!

Was told by an attorney that we are age discriminating if we put an age restriction on gym use.

Word it as “Persons over the age of 16” - you are not referencing familial status that way.

I would get with you company legal counsel on this. There have been a lot of lawsuits where a specific age was posted for the common areas and amenities.