It appears to the researcher that Luke Nickerson, Luke Nickelson, Luke Nicholson, John Luke, and John Lake are the same person. It was not uncommon for people to be known by more than one version of a name.
From ”Maine Revolutionary Pensioners” by Flagg (Pejepscot Historical Society)
Luke Nicholson, list 35c, service: Mass. Line, Rank: Private, age 83, Cumberland Cty., died May 4, 1829
From “Harpswell in the American Revolution” (call no. M18-14, Pejepscot Historical Society)
“Nickerson, Luke, Harpswell, Pvt. Capt. Reed’s Co., Col. Brooks’ rgt.; Continental Army pay accts. for service from Jan. 12, 1777 to Jan. 15, 1780; residence Harpswell; credited to town of Harpswell; also Capt. John Reed’s Co., Col Alden’s rgt., return dated Jan 12, 1778; mustered by Col. Sewall, Muster Master for Lincoln County and by a Continental M. M.; also Capt. Reed’s Co., (late) Col. Ichabod Alden’s (6th) rgt., return of men who were in camp on or before Aug. 15, 1777 and who had not been absent subsequently on furlough, etc., certified at Cherry Valley Feb. 24, 1779; also same Co. & same rgt. muster roll for March and April 1779, dated at Cherry Valley, enlisted Jan. 15, 1777, 3 yrs.
From Brunswick Town Clerk’s office, veterans card file, 1941:
Luke, John, Brunswick (Cumberland Co.) Me., Revolutionary War
Growstown Cemetery, Grave 1
Grave marked by field stone known to the owner of the Prop. E. J. Alexander.
[researcher's note: this appears to be the farm where Luke was buried in West Brunswick, not actually Growstown Cemetery. Perhaps the record was kept with Growstown records for convenience.]
Sources: Sol. & Sailors of Mass. Vol. 10, page 31. Mr. Munson S.A.R.: John Luke (a Negro) list of prisoners brought in the first cartel from Rhode Island as returned by John Ayers dated Providence Jan 18, 1779. Reported as mate.
SAR [Sons of the American Revolution] cd-rom, copyright 2000, Revolutionary War Soldiers
Luke, John, Private, buried Growstown Cemetery
same source (SAR cd-rom)
Lake, John, soldier, buried Growstown Cemetery