GLF5 Captain describes a near runway incursion at L11 and Runway 8R. The clearance from Ground Control was to exit the Northeast cargo area and taxi via Taxiway L. Ground Control caught the error in time to prevent the incursion.

Narrative

Due to heavy traffic volume at the MIA FBO; remote parking operations were in effect. This required all large corporate jet operators to use the Northeast cargo base area. Upon repositioning from the Northeast cargo area to the FBO for passenger pick up; we were instructed by Ground Control to taxi on Lima to Zulu and hold short of [Runway] 8L. As we pulled out of the Northeast cargo area the flow of traffic (yellow painted lines) [taxiway lines] has you heading south to exit the area. This lined us up directly for Taxiway L11. As the non-flying pilot I was heads down running the Taxi Checklist. Almost directly after exiting the Northeast cargo area; Ground Control gave us an immediate clearance to stop and hold position. When I looked up I noticed that we were on Taxiway L11 heading for the Runway 8R (an active runway at the time). At no point did we violate the safety area of Runway 8L. Without Ground Control's call to stop and hold position I can see a potential situation develop where a pilot would taxi across an active runway (8L). Upon further examination we did not notice any taxiway markings or signage that would help anyone avoid this in the future.