A phrase used in "An Experiment concerning the Spirit of Coals", a letter to Robert Boyle from John Clayton.
Its literal meaning would be that the preassure created during the experiment was enough to breeak the "lute", which was a substance used to make seals between various chemistry apparatus (1)
A more modern use of the phrase thats recently started to recently arise, is to use it as an alternative to "grinds my gears" (2)
(1) "At first there came over only phlegm, afterward a black oil, and then likewise a spirit arose which I could noways condense; but it forced my lute, or broke my glasses" - An Experiment concerning the Spirit of Coals, a letter to Robert Boyle from John Clayton
(2) "Ya know, it really forces my lute when people dont read the pinned comments" - Technology Connections : Pressure lamps: gaslighting on the go