doesn't this ruin the handling and enjoyment of driving an MX5?
Not necessarily but it depends on what you enjoy or hate. If done properly, the car should still be enjoyable to drive. However, if it bottoms out on dips, scrapes over speed bumps and driveway entries, has \"darty\" handling characteristics and rides like a dray, you may tire of it after a while.
Should I stay away from used MX5s that were lowered?
Were or are? It comes back to personal preference.
.....does that mean that it can be adjusted to bring the car back to the original position?
Not necessarily. It depends on the type of suspension installed. Some are designed to be completely height adjustable but adjusting others may result in some change to damper stroke which, in turn, may compromise the intended ride/handling setup and result in undesirable characteristics.
However, if you have one that has a system you don't like, you will probably have little difficulty selling/swapping the suspension to replace it with OEM specification stuff.