I don't see it happening. In order to grow cells, you have to replicate the conditions that exist in the cell's natural environment--the salts, hormones, amino acids, sugars, etc. And you have to maintain an absolutely sterile environment, which would be quite a challenge in the weightless environment of space. Plus, growing cells requires supplies, lots and lots of them. I doubt that I've grown even close to a pound of cells in my career, but I've probably generated hundreds of pounds of trash doing so, not to mention the gallons and gallons of discarded liquid.
For long-term space flight, you'd probably want to set up a small ecological system, not try to establish some sort of lab for growing cells.
Thanks.
“Nevermind,” in my best Emily Litella voice. :)