I would not call any short reset trigger DAO. That second shot on a Glock or LEM after a tiny reset is certainly not a "double action". There is only one action performed at that point, since the striker or hammer fully cocked after each shot.
The LDA, like the LEM, Daewoo Fast Action/Double Action + and FN's SFS are all systems that use completely cocked mainsprings with uncocked hammers. In terms of pre-cocked springs, they are arguably SA. The fact that the hammer is out of position is nifty, but somewhat meaningless. More of a nice feeling than an actual mechanical safety mechanism. FN first came up with this idea in the early '80s, before the Glock came out. It is the granddaddy of all the pre-cocked mechanisms that followed.