Bring a large pot of salted water to a boil. Add the lobster tails, lower the heat and simmer for 8 minutes. Transfer to a work surface.
In a small saucepan, boil the orange juice and shallot over medium-high heat until reduced by half, 2 to 3 minutes. Remove from the heat and stir in the orange peel, lemon juice and salt. Let stand for 3 minutes, then strain the mixture over a bowl, pressing to extract any liquid. Return the strained liquid to the saucepan, place over low heat and stir in the butter, 1 tablespoon at a time, until incorporated. Cover the sauce to keep warm.
Using kitchen scissors, slit the lobster tails and pry out the meat. Halve the meat lengthwise, then cut crosswise into thirds. Thread the meat onto 4 skewers and place in a shallow serving bowl. Pour the orange-butter sauce over the lobster skewers just before serving.