I'd really have to see your left hand to know what to suggest. I could be a result of poor positioning, pressing too hard on the strings or just that you are playing pieces that are too difficult for you. Another cause of left hand tension is due to the instrument itself. With the guitar, which I also play, the default left hand position allows you to play with the finger joints in mid range position most of the time. With the lute this efficient default position cannot be employed as much because you have to get more up on the finger tips due to closer string spacing. The trick here, I've found, is to be aware of when you can play in this efficient default position, and then do so when you can. The position I'm talking about is this. 1) hand parallel to the neck 2) relatively straight wrist 3) all finger joints curved in a mid range position. For this position you must get the neck raised up to about a 45 degree angle. I don't know if this violates some rule about historical performance or not, but it's good for the hand.
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