Boro earned a valuable point that kept them five points clear of United at the top of the Barclays Premier Reserve League North.
Lee started along with Stuart Parnaby and Chris Riggott who were both continuing their returns from long lay-offs.
United scored on the hour but the lead was cancelled out by a superb long-range effort by Ben Hutchinson, who had replaced Lee at half time.
Boro team:
Turnbull, Parnaby (Johnson), Riggott, Hines, Williams, Bennett, Walker, Kennedy, Goulon, Lee (Hutchinson), Graham (Thompson).