John Lightfoot on Matthew 6:3

[Let not thy left hand know what thy right hand doth.] He seems to speak according to the custom used in some other things; for in some actions, which pertained to religion, they admitted not the left hand to meet with the right. "The cup of wine which was used to sanctify the coming in of the sabbath, was to be taken with the right hand, without the assistance of the left." "Let not man receive into a vessel the blood of the sacrifice, bring it to the altar, or sprinkle it with his left hand." And in the same tract, it is related of Shammai, that he would feed himself only with one hand.