Salvete!
When you're picking a lute, look carefully at the pegs and frets. On a "real" lute. the pegs will be just that- pegs stuck in holes in the pegboard. If the pegs & holes aren't individually, carefully fitted, the strings will slip with great regularity. This makes a really good lute quite expensive- I talked to one gentleman who restores stringed instruments, and he said he charged about $200 *per peg* to fix a poor fit. If you've got an 8-course lute, that's 15 pegs. Be careful with really inexpensive lutes, as they're usually made "assembly-line" fashion and fit isn't that good. The instrument I play (which belongs to my college; I can't afford a nice one of my own yet) was made that way, and cost about $800. Whenever it gets rather damp or dry, I have a lot of trouble with keeping it in tune for that reason. Also, the frets on a "real" lute will be tied on, actually wrapped around the neck of the instrument. They sometimes slip, too, and need to be re-tied. (This may not be a problem on a higher-quality lute; it is on the one I use.)
Your alternative to an authentically constructed lute is to get one made with guitar construction. If you're not terribly concerned with historical accuracy, this might be a better idea. The pegs are the screw-type guitar pegs, and frets are inset. Keeping these in tune is easier, and (though I'm not positive) I believe they might also be less expensive than a comparable-quality "real" lute, because the pegs don't have to be individually carved.
And, on a lighter note:
How do you define a lutenist?
A musician who spends half their time tuning and the other half playing out-of-tune.
Good luck! Prezmyra