LO (and others)
The main issues, in my view, with a separate lift engine were these:
1. A separate jet lift engine had to use hot air to develop thrust - that's inherently less efficient than using cold air. That reduces the basic efficiency (and weight) advantage of a separate engine.
2. A hot engine exhaust located towards the front of the aircraft will inevitably introduce hot gas ingestion effects. As LM have shown, the cold lift fan provides a useful way of helping get past a very serious problem.
Having looked at a couple of papers recently, it looks as if the Gas Coupled Lift Fan (GCLF) was a very serious contender within NG/BAE until late in the day, when it became clear that the piping and ducting required to drive a large (c. 18,000 lb thrust) fan would place too much volume demand on the fuselage design. LM appear to have gone fro shaft drive from early on.
As I've said before, the designers have to make some very big calls early on for powered lift aircraft. In my view, LM got most of them right, given the requirements they had to meet. Others are happily invited to disagree.
Best Regards as ever to those working the sums,
Engines