Can you feed a sub panel from a timer for outside lights?
Yes you can, as there is nothing in code that would prevent you from having a timer on a sub panel.  If it located on the home or a attached garage you are not required to add additional grounding electrodes, just take a 4 wire feed (2 hots, neutral, and ground) to the sub, or, if you run the feed in metallic conduit, the conduit can be the ground. Neutral needs to be isolated from ground; most panels today already have this, don’t add the neutral to ground bonding screw (it is a green screw, usually shipped in a bag); if already installed (that or a jumper), remove it so the neutral is isolated as required by code.