I'm a big believer in simplicity.
If you're trying to determine a starting value or even a max value of something like player lives, turns and so forth. Then this is where statistics and research come into play. Simply testing the game with players, analyzing the results and comparing it to similar games can help you find the sweet spot for anything.
There is no need to dive into the psychology of the human mind to find out how many lives players should have. You should, like statistics, let the data speak for itself and tell you that sweet spot for any given mechanic or system.
For example with unlimited turns: 80% of players completed this puzzle in 10 turns or less on the first time of playing the game.
With that piece of information, I have a pretty good idea of the turn value for that particular puzzle for first time players. Everything else falls into place and adjustments can be added later based on the actual players and not some research paper.