Was there ever a LEGO store in Miami International Airport?
I couldn't find any mention of a full LEGO store in MIA on the web.  Looking at the other logos that are recognizable I would guess that they don't represent full stores, but products available in the existing stores.  I doubt Jack Daniels and Johnny Walker have free-standing stores in the airport.  I don't see any sign that Jack Daniels has any free-standing stores.

There is a Mindworks Toys in MIA which probably sells LEGO sets.  I'd guess that's the source of the logo for this sign.