I'm not sure it is a handedness thing. They have 8 D right now, 4 L and 4 R. When Liles was out they moved Kevan Miller to left and basically used those same 6 defenseman for all of Liles' absence. Morrow, a LHD, didn't play a single game.
We'll see how it plays out over the next few games, but I think they simply feel like Liles is their 5th or 6th best defenseman and C. Miller is 7th. They've set up the D where they have a shutdown, 2-way pair (33/25), then 2 pairings of offensive minded player with a "stay at home" guy. Miller and Liles fall under offense, but they feel safer with the veteran Liles. I don't want to get them in trouble for something that hasn't happened yet, but any extended run with Colin Miller in the pressbox would be the team not icing their best possible lineup.