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For the strip steak: Heat a water bath with a sous-vide circulator to 130 degrees F.
Place the steak, thyme, shallot, salt and pepper and 2 tablespoons of the lemon butter in a vacuum-sealable bag. Reserve the remaining lemon butter for another use. Vacuum seal the bag and simmer in the water bath for 30 minutes.
Remove the steak from the bag and reserve the juices and contents. Heat a cast-iron skillet or heavy-bottomed saute pan over high heat until very hot, then sear the steak for 30 seconds per side. Remove the steak and let rest.
Add the reserved cooking juices and contents of the vacuum bag to the skillet and reduce by half. Pour over the steak when ready to serve.