"lock-in" implies some sort of lock. "I don't won't to leave because the service saves me so much money" is not a lock, you can leave, you just choose not to be

"lock-in" implies some sort of lock. "I don't won't to leave because the service saves me so much money" is not a lock, you can leave, you just choose not to because it's better for you to stay. And if the vendor increases his price you can just take your data and go - your same application will run on another vendor's hosted MySQL instance. If I say I'll pay you $1 if you sit in my office for an hour, you can't say that you were "locked in" by me, if Mary offers you $2 to sit in her office, you can walk over to her office and get more money.