A client came to us with a load balancer configuration old enough that the person who set it up had left the company years earlier, and nobody wanted to touch it. It worked, which was exactly the problem — there was no appetite for a maintenance window to replace something that wasn't currently broken.
We ran the migration in parallel instead of in place: stood up the new load balancer alongside the old one, mirrored a small percentage of read traffic to it for comparison, and gradually shifted real traffic over using DNS weighting once we'd validated behavior matched under real load.
The whole migration took about three weeks and had zero customer-visible impact. The old load balancer stayed running, untouched, as a rollback path until we were confident enough to decommission it. Slower than a maintenance window would have been, but nobody had to explain a scheduled outage to their customers.