Andrew:
For me, the question of whether it makes sense to lay up on a par three would be dependent on the situation. If I'm just playing a Saturday morning game with buddies, no way am I laying up, regardless of risk, unless I physically cannot carry a hazard with even my best Driver. Now, make it a tournament round, and that is a different story and would depend on the circumstances and type of tournament.
The best example of a potential lay-up par three that I play regularly under tournament conditions (club championship, etc.) is the 5th hole at my home club, Settindown Creek. It is a 190 yard par three with a narrow but deep green that has water just off the right edge and a deep bunker left, but with an area for a lay-up type shot short and left of the green. Going for the green is definitely the most intimidating shot on the golf course.
If I'm playing the hole in the medal play club championship, I will most likely play to the lay up area, in order to take a double bogey or worse out of the equation. In a match play tournament, the decision gets more complicated. If I have the tee, I will play for the green if I feel good about my iron game that day but be perfectly content to lay up if I have any doubt, as I still have a good chance of halving or winning the hole from the lay up area. If my opponent has the tee, my decision would most likely be dictated by his shot. If he hits a good shot on the green, leaving a sure par or possible birdie, I'm almost certain to go for the green. If he goes for the green and puts it in the water or bunker, I'm almost certain to lay up. If he lays up, its depends again on my confidence level on the given day.
The other factor that comes into play here is where in the round the potential lay up par three falls. If the 5th at Settindown were instead to fall as the 17th hole, I suspect my decision as to whether to lay up or not would be significantly altered based on the status of my match or medal play round.
I personally think that a par three such as the 5th at Settindown, that brings a lay up option into the equation because of the severity of penalties for missed shots as opposed to sheer length, is a good hole. The same is true of the 2nd at Dornoch, and I have seen many mid to high handicappers make that play. I am curious to hear the circumstances that caused a player with your game to lay up on the 2nd at Dornoch, presumably in the Shield. Obviously it worked out, as you won the hole.
Mike