My HOA is also dealing with this now. Our's are 35 years +_. You don't replace the elevator; you upgrade the lift and mechanicals by taking the parts out, re-machining them, and then putting it back together. At the same time, there are electrical and fire code upgrades that have to be done. If you are lucky, the process can be done in 4-6 weeks. Not so lucky; it took our last one 3 months with handicapped folks unable to get down the stairs for that entire time. We are trying to do this proactively with advance notice so residents can make other living arrangements (take a vacation, stay with family etc), but the elevator company (probably the best known one) has been awful to work with. They own the parts, but we have now switched companies.
Cost in 2016 was $135000 with 2/3 of that the actual elevator and the rest the upgrades required. In 2022, additional fire code changes have added to the cost. The one finally finished in Jan (down payment made in spring of 2023), cost $150,000 for the elevator + $100,000 for the fire code upgrade changes needed. With the elevator, there is a fire panel that runs the fire alarms etc. When that is changed, all the other changes also have to happen. We don't have a bid for the next one yet, but it will likely be more. We've had to go back in and fix some of the work done on the fire code upgrades; there was a reason that company was $150,000 lower...
With any large scale project, the standard is a 50% down payment which allows the company to buy the parts and get things moving. That's when you get on the schedule. If the HOA doesn't have that money to front while the special assessments are coming in, you might want to take a closer look at the amount of reserves.