Clearly whatever the airspace design, arrivals have to cross departures somewhere. Choosing the least inconvenient place is of course the key.
As a former airspace planner I hope LAMP will be successful. However the recent rumpus over the Gatwick ADNID trial gives an indication of the resistance to changes in flight paths, however 'green' they might be, from those living below them. A clash between what is technically possible and what is politically allowable has always existed but is more severe than in the past. This could end up scuppering significant parts of LAMP. I hope the various stages are not too inter-dependent.
Regarding fuel savings that airlines might achieve by earlier climbs. Our flight deck friends might contradict me on this but I suggest an airline does not make its fuel calculations to the degree of detail of will a flight departing Heathrow get continuous climb or will it have to wait until Detling before leaving 6000'.