All a star, or a main sequence star, at least, is is a ball of hydrogen which fuses it into helium in its core. So if you manage to generate hydrogen fusion in some sort of chamber, yes, that's pretty much what a star is.
The problem is, of course, that the temperature for fusion is ~10 million kelvin, and containing something that hot is a bit of an issue. As soon as fusion ignites, there will also be a ridiculous amount of pressure, coupled with the temperature, which make it difficult to create any kind of self-sustaining laboratory star. But, assuming you have some super strong material, then yes.