I don't think Lloyd is a good enough climber to be KOM at both races. We must remember that the Giro is very stingy with its mountains points, with only the first three or four riders across the stripe getting points. Also, the first across the line gets proportionally more in comparison to second and third than in the Tour.
Also, Lloyd simply isn't an elite climber. He could hold the Tour KOM for a few days but he isn't going to win it. He won the Giro's KOM the same way Fabian Wegmann won it; hoovering up the 3s and 5s available for 2nd and 3rd category climbs, and breathing a sigh of relief that no major name went hunting for points the way Sella, Garzelli and Piepoli have done in recent years; the only names that seemed to want to challenge him were Tondó (ran out of steam in week 3) and Pozzovivo (dropped out in week 2), as they were the ones fighting him for the points in the stage 11 breakaway; Lloyd was also dropped before the last climb and it was up to Bakelants and de Greef to protect the points from Tondó. With the double-points available for MTFs in the Tour and the wider disparity between 1st and 2nd category climbs (16 and 10 points available for first rider) and 3rd and 4th category climbs (4 and 3 points available for first rider) it would be very, very difficult for Lloyd to duplicate that success.