The only way the new dental insurance plan would know about how much of the lifetime maximum you have used would be if the other insurance plan transferred that data. There is no national database.
The only time I know that this data was transferred was because I was switching between different types of plans inside the same insurance company, or when my employer picked a different provider. We were told these dental and medical maximums were being communicated. This was pre-ACA. The ACA removed most maximum caps, but not those related to adult dental coverage.
Some companies/plans don't have a lifetime cap. So they would be unlikely to transfer any data they have to the next insurance company. When changing employers I have not been required to tell them who my previous insurance company was.
The only time I ran into an issue where the current dental insurance company need information about a previous expense was when a crown was being replaced. The new plan wouldn't cover it unless it had been at least 10 years. Their explanation was that if it was less than that it was being replaced as part of the same "event" but if it was older than 10 years it was a repair of the crown. It was older, so it was covered.
If you have a new employer but the same insurance company, then it is likely that the lifetime cap will still be tracked. The cap isn't tracked by the dentist, it is only tracked by insurance companies. The dentist will recommend procedures and then the office staff will help you determine the cost of those procedures in advance. But the office doesn't know if you have met your deductible or if you have reached a yearly or lifetime cap without checking with the insurance company.