As far as I know, glass is a non-crystalline amorphous solid. Does glass exist in crystalline forms? Or is it the definition of glass that it's non-crystalline, in which case my question is based off of a false assumption?
As Ivan explained, a glass is by definition amorphous. However, you can take a quartz crystal (silicon dioxide, which is the main ingredient of glass) if it is of high purity and optical quality, and machine it into a transparent object such as a window pane.
"Lead crystal" usually refers to glass cut decoratively to partly resemble the facets of a cleaved crystal, so it's not really misleading, considering that most people recognise crystals by their faceted shape rather than their internal structure.
I looked into "crystalline glass" after being astonished at this term in a promotion involving what looked like ordinary glassware, with no flat surfaces. In European rules, "lead crystal" implies more than 24% lead oxide in the formula. There have been concerns about lead leaching from lead glass, so that alternatives such as barium have been replacing lead. Manufacturers are permitted to call low-lead or "lead-free" glass "crystal glass" or "crystalline glass". That seems a gross deception in the case that drew my attention, but in glass with similar designs to cut lead glass, perhaps not, although "crystalline" still seems more of a misnomer than "crystal".
Glass is by definition amorphous. If you were to crystallize it then it would be considered a ceramic, even though compositionally you have not changed your material. Often times the crystallization may occur as a result of slow cooling rates which then allows the formation of ordered arrangements of atoms (crystals) which are usually disallowed by more rapid cooling.
Sometimes partial crystallization occurs and is even desired. This produces a "glassy-ceramic" material which can give the best of both materials. Corelleware is famously strong and durable because its structure consists of ceramic particles in a glass matrix. This also gives it it's famous million needle-like shards when broken.