Is there any standards of the solid content of lubricant ? Or maybe rules of thumb that can predict when the lubricant should be changed (from solid content)

Are you looking for particulate contamination measuremants ?

If so, ISO 4405, ISO 4406, NAS 1638, SAE 4059 are the standards used for the same.

Generally the equipment manufacturers specify the maximum allowable contamination levels for their systems.

Specify your application and type of fluid

Cleanliness standards, ISO and NAS are usually measured by particle counting and are generally used for hydraulic systems and turbines.
i.e. for clean systems, with results first measured as parts per million for size ranges and then for ease of identity into a code(ISO, NAS).
For other systems the solids are filtered and weighed(millipore solids)
This weight would include all insoluble material, wear debris, solid contaminants etc.
Limits depend entirely on the system involved.For high pressure servo valve hydraulic system high levels of cleanliness are needed and general recommendations are available via component manufacturers and filter suppliers.