Lying down as quickly as possible (4,3)
I believe the answer is:
flat out
I believe this is a double definition.
'lying down' is the first definition.
(laying flat on the ground)
'as quickly as possible' is the second definition.
(as in working flat out)
(Other definitions for flat out that I've seen before include "Exhausted - at full speed" , "KO'd" , "Ready to drop" , "At top speed or effort - being horizontal?" , "full tilt?" .)