John Lightfoot on Luke 7:5

[He hath built us a synagogue.] I. It was no unusual thing for one single man to build a synagogue at his own charge: "If any man build a house, and afterward consecrated it to a synagogue, it is of the nature of a synagogue." Gloss: "Any one that builds a synagogue and gives it to his fellow citizens," &c.

And the doctors in that treatise dispute much upon this question, Whether it be lawful to sell a synagogue or to alienate it to any civil use: and amongst the rest, they suppose some one building a synagogue, but would at last reserve it to his own proper use.

II. They had no scruple as to a Gentile's building it, since the holiness of the place consisted not so much in the building as in its being set apart and dedicated to holy use; of which we have some instances in Herod's building the Temple. Such a one had this centurion approved himself towards the Jewish nation, that concerning his liberality and devotion in being at the charges of building, they found no reason to move any scruple.