What does 'L' mean in the name of motor driver IC "L293D"?
Not much. It's just a part number, originally from the European company SGS-Ates.  

Perhaps at one time it indicated "Linear" (most of the chips SGS made were bipolar linear and started with an L or an T). With all the mergers over the years, any such meaning would be long gone from those 30-40 year old designs. 

When SGS made clones of then-popular parts such as the \$\mu\$A7805 and \$\mu\$A709A they called them L7805 and L709A so you could say it's kind of a marker that points out the manufacturer (SGS-Ates, then SGS-Thomson, now ST).