Any suggestions for how to remove the knobs so that I can replace the cartridges (Lasco S-180-1NL 4001)? There are no screws. I am able to loosen the knob from the counter top by unscrewing from underneath the sink, which allows me to raise the knob up a bit so that I can unscrew the silver disk you see in the photo that is below the gold part of the knob, but I don't get further than that. The knob stays attached to the fixture and I can't get to the cartridge. Thank you]1
We have pretty much the same ones. The top chrome part should pop off and the screw lays on the top. That screw removes the entire faucet handle.
I take flat head screwdriver to the edge and it pops off. Not exactly easy. But it will come off.
I've had to replace 3 sets of these units, and it was an absolute nightmare, good luck!
The top is either a pop top or screw on and I've found some diagrams detailing the breakdown but if you know the exact manufacturer and model then it's likely on their site (but that's an easy solution and finding the manufacturer's stamp isn't always easy ... not everyone is like Kohler and brands it up front, a lot of knock offs that want to look like a competitor and therefore hide or don't even attach their "brand" on the product).
So, to solve the problem ... look for a small tab or notch on the chrome top (as small as the notch on your cell phone to pry it apart) and use the same type of hard nylon prying tools to pop the top off. If it's a screw on then a strap wrench might be of use although there's not much to grab onto. Using the nylon or protected screwdriver, gently pry up from the sides under the chrome top to see if you have any "give" (muscle it and you'll bend the chrome, be gentle and be patient). If you need to make your own protective rubber coated tools, the paint section of your local Home Depot, Lowes, etc. has a plastic coating meant for handles ... use it on the other end to safety coat a screw driver for example.
I found a site with similar products at https://www.plumbingsupply.com/images/valley-bathroom-faucet-y28428-chrome-pol-brass.jpg so giving them a call will likely yield you and answer directly from them, especially since they sell repair parts too and that means they have people that know how to take it apart and identify your product. They don't display their contact phone number but they are located in Chico, CA and here's their contact page: https://www.plumbingsupply.com/cgi-bin/feedback.pl?t=contact