Here's something that has helped me enormously on lag putts: Don't look at the ball during your practice strokes! Don't look at the putter head! Look at the intended target.
As a drill, I set up for the putt, get my line, and before I roll the ball, I focus on a spot on the line or focus on the hole (depending on the situation) and then just rock my shoulders WITHOUT looking at the ball. This helps me roll it close (usually) or even occasionally in the hole! Very good for distance control and not bad at directional control.
I don't recommend doing this during the stroke, however, because you will occasionally mishit a putt off the heel. But it's great to do as a practice stroke or even a pre-round drill.
Try this as a drill when you're practicing to see if it helps you; I like it so much as a drill that I started using during play.