To be technical, the orignal 1911, did not have a beavertail grip safety and a beavertail could not be fitted to it without modifying the frame. It did not have a "commander" type hammer, did not have speed bumps, did not have a high cut at the trigger guard and really wouldn't feed hollow points very well. It did not have extended thumb safeties, and they had a curved backstrap. And they didn't have any kind of firing pin block. So if we are going to be technical, there are few 1911 "type" pistols that could be called a 1911.
Some manufacturers use a reverse plug for the recoil spring and guide rod on some models and yet they call them 1911s. Some have added tactical rails to the dust cover. Some have grip safety firing pin blocks, some have trigger activated firing pin blocks. Some have full length guide rods that would not work in the "original" design because the recoil spring cap has to be open instead of closed. Yet in all of these variations, they are commonly referred to as 1911s - even when the parts won't work in the original design.
The LDA is a bit different, but it is simply a DA trigger on a 1911 platform. If we accept all the other variations of the 1911, how can we say that the LDA is not a 1911?