I can’t speak to NEA contracts, but I can to at least some teachers’ pensions. In the school district where I taught, there was no “lifetime medical insurance”, quite the opposite. When I turned 65 and switched to Medicare (I was still teaching at the time), the district paid for my Part B and Part D expenses. They averaged about $300 less per month than the district’s provided health plan. No, I did not get the extra money, in fact my income for purposes of my pension was decreased by that amount. One reason I retired at 66 was it no longer made economic sense to keep teaching.
I was speaking to the California plan, which will be every state should the NEA have their way.