Eurostar have to allow for stops at Ebbsfleet and Stratford, so something will have to give.
Lydd are talking of plans to handle upto 2m pax pa, with long term plans to go as high as 6. The blurb on their website seems to focus on turboprops and regional jets, but doesn't really explain why they'd need a runway extension for this.
It even goes into great deal about the airlines which might be interested in using it.
As a reliever to LGW, LYX has to be more promising than MSE, but I think LGW would have to get very very full before airlines really want to go so far out of the way.
I could see a scenario developing where the nimbys get there way, and capital investment on new runways at LHR or STN doesn't look likely to produce a return, and 2019 cap on LGW stays on for longer - but I think a mass defection to LYX would still be a long shot, considering how many airports London already has.
Even if high speed domestic trains make Lydd closer, do people really want a train + bus connection? LTN is bad enough as it is getting in and out of Parkway - if people are going to use public transport, there needs to be a station right underneath, or immediately outside, the terminal - and even if there are railways near to LYX, then they would need huge volumes to make the investment worthwhile.