Being called photo labs doesnt mean they use the Lab colorspace. They're called labs cuz developing and making prints from film (used to) require a whole bunch of chemicals.
In fact, Lab is not a true definitive colorspace at all. It's the digital interpretation of what we humans perceive as spectral color. All colorspaces (sRGB, AdobeRGB, prophoto, CMYK, etc..) are translated into Lab (digital) mode when they're digitalized. It's the only way the computer knows how to do calculations on the relationship between hue, saturation and luminosity.
Most commercial photo labs' machines operate in the sRGB colorspace, but inkjet has long surpassed sRGB in terms of potential color reproduction.
In home printing, it all boils down to hands-on experience in printing on various paper, using various inks, and taking courses in color management if you want to get good prints.