One I can think of is related to RDS - if you run your own MySQL instances, you can pretty easily migrate away to another set of (MySQL) machines by replicating off the master onto a new slave, and then promoting the slave to master and shutting down the original master. RDS doesn't allow (external) replication, so your only option to get away from RDS altogether is to do a mysqldump, which can get nasty if you are trying to migrate away without downtime (a full export/import via mysqldump can take a long time, and you'll miss any updates during the process). At the very least, it involves either a chunk of downtime or a decent bit of manual migration, which is unfortunate.
That said, I don't think they set it up this way to specifically cause lock-in, it's just technically difficult to allow users to manually manage replication alongside RDSs automated system.