What it is
The Ames LF4000B (4000B in the leaded version) is a lead-free silicon copper reduced pressure assembly in ½" through 2" with top-mounted test cocks, ball-valve shutoffs, and an internal relief valve that discharges from the bottom. It serves the same domestic, irrigation, and light commercial work as its Watts cousin and is spec'd where Ames has the relationship.
Length and height match the Watts 009 size for size: 10¾" at ¾", 21⅜" at 2", 3" to 4½" above centerline. Below the pipe it is shallower than any other small RP: 1½" at ¾", 3¼" at 2".
What matters for the cover
Same covers as the 009. If your counter stocks for the Watts 009M2QT, those covers fit the LF4000B: the 20 × 20 at ¾", the 24 × 24 at 1", the 30 × 24 as the closest fit at 1¼" through 2" with the 36 × 24 in reserve for a 2" with a strainer.
Shallow but still an RP. The relief valve is inside the body, but it still discharges downward and Ames calls for the standard air gap and drain clearance. The relief valve under the body has to drain. Set the cover so the base closes to the pad around the assembly but never seals under the relief port.
Strainer adds length. The optional inline strainer pushes a 2" toward the 36 × 24.
Do not confuse it with the 4000SS. The 4000SS is the 2½" through 12" stainless RP. Different assembly, different covers; the finder has both.
Stocking
Ames-spec markets are regional and often follow a consulting engineer's habit. Where they exist, the LF4000B moves in the same ¾" and 1" volumes as any small RP, and backflow testers who service Ames-heavy client lists benefit from carrying the 20 × 20 and 24 × 24 as truck stock. Because the covers are shared with the Watts 009, there is no separate bin to justify.