The two-piece handle likely means this is a later production unit made in Taiwan, before they switched back to USA builds. The USA-made Lincoln jacks came with one-piece handles. I’d take it apart and measure the main seal (Bore is slightly larger on this one, at least on mine)— the seal in most kits may be a few millimeters smaller than the American versions, it fit on the ram fine.
I have the same jack, and the standard rebuild kit main seal wasn’t large enough. That project is sitting on the back burner for now. By the time I figured out the issue, I picked up another Lincoln made in the USA, ordered a new kit, and got the larger seal. HPC was able to source the seal for me. Hydraulic Parts Supply in Sawyer, KS: (620) 594-2247. Old-school hydraulic parts shop — you have to call to order, but they are helpful and can answer questions. Good news, you can take the ram apart with a 46mm or 1 13/16 socket, the older model with the gland nuts are harder to take part. Post some picture of the rebuild, it is a nice jack worth a rebuild kit.