Based on the description—a young, mostly grey bird with a bright red hooked beak, long wings, a long tail, and a patch on its crown, spotted in Lincoln, Massachusetts—the bird is likely a juvenile Red-tailed Hawk (Buteo jamaicensis).
Why It Fits
Size and Appearance: Red-tailed Hawks are large raptors with wingspans around 4 to 5 feet. Juveniles often have mottled, paler plumage compared to adults.
Beak: Like other raptors, they have a sharp, hooked beak used for tearing prey. It is typically dark, though lighting can affect its perceived color.
Wings and Tail: Their long, broad wings support effortless soaring, while the long tail aids stability in flight and when perched.
Crown Patch: Young Red-tailed Hawks frequently show a pale patch on the crown, sometimes called the "capital patch," which usually fades as they mature.
While these traits strongly suggest a Red-tailed Hawk, confirming the identification with a local field guide or birding expert is always a good idea.