This machine includes a base frame (17) and a lens support (19) mounted on the frame (17) with the lens support (19) having elements (29A, 29B) for driving a lens (15) into rotation around a first axis. It includes a tool holder set (21) including a rotary shaft (39) around a second axis (C-C′) and elements (43) for inclining the first axis (A-A′) with respect to the second axis (C-C′). The rotary shaft (39) bears at least two tools (49, 51) for machining the lens, spaced out along the second axis (C-C′), and a spacer (50) positioned in an intermediate area (55) located between both machining tools (49, 51). The spacer (50) defines an outer surface (57) for machining the lens.