Full-swing grip: This will help improve your distance control on long putts.
When you're facing a long lag putt, you need feel to roll it close to the hole. This is not always easy to achieve when using a conventional, one-piece pendulum-like stroke. Because of the way you grip the putter, the club, arms and shoulders move in unison, and the hands and wrists stay passive -- more suited for short and medium-length putts. You need some wrist action to create feel to hit long putts close.
Here's a tip I learned from longtime student and superb putter David Frost. Take your normal putting stance, but switch to your full-swing grip. This will automatically give you more wrist action in your stroke and encourage much better feel. On a long putt, there needs to be a release of the left wrist (a cupping) just after the putterhead makes contact with the ball.
With most shots, wrist action is an essential ingredient for feel, and I believe adopting this grip change will improve your touch. You'll get those long lags close enough for an easy two-putt.