What does my rogue have to learn to be able to pick locks?

Your rogue's lockpick skill is dependent on your cunning attribute. The Lockpick skill in Dragon Age 2 improves with every 10 points you spend in cunning. In fact on your character record if you look at the attributes and highlight cunning it tells you this.

Help Guide Says:

All locked chests in Act 1 are of Standard grade at maximum, which requires 20 in Cunning to unlock. If you have a rogue as a permanent fixture in your party, there’s profit to be had by boosting this attribute at a fairly early stage. Complex chests that require 30 Cunning appear from the start of Act 2, so you may also wish to begin investing attribute points in anticipation of this. Master chests require 40.