For LX, London is not going to generate any connecting traffic (unlike BA). LCY is a much more pleasant airport and compares with LHR even if you are going into West London. You can be off the plane and on to the DLR within 5 minutes of landing. The DLR is quick and reliable and you can connect to the Central or District lines to get into West London. Frankly it's going to take you the better part of an hour whether you're going from LHR or LCY and the latter is a much more civilized airport. Remember also when leaving, you can arrive at LCY just 15 minutes (though I prefer to count on 30) before departure. At LHR, I wouldn't want to arrive less than a good hour (even without bags).
Don't get me wrong, I use both LX and BA (also U2) with London as a final destination, but LX have a decent product and I like being able to use LCY.