Can I continue to use my old Lexmark E342n with macOS 15.3.2?

Welcome!

Lexmark was always inconsistent on MacOS support. It's hard to say, but I am not hopeful. This Lexmark page:

https://support.lexmark.com/en_us/drivers-downloads.html?q=Lexmark%20E342n

shows the last driver updates for Mac were 12 years ago. That is mid-Paleozoic in computer years. They also say all support inclduing phone suport has ended for that model. Even the users' guides are no longer downloadable.

Have you actually tried it with your new Mac? I serious doubt the printer has AirPrint capability, but you have a slim chance with a wired connection. With the guides gone, I cannot tell what connectivity ports yours has, so look at this:

Add a printer to your printer list so you can use it on Mac - Apple Support

If you are not sure what port the printer has, take a picture of the ports and post it here using the "Image Insertion" tool:

Image files uoloaded must be 5MB or smaller, and in either jpg or png format.

However, I think you will be shopping for a newer printer.

You will need to see if Lexmark still is developing drivers for the E342n that are compatible with macOS Sequoia. No Lexmark E-series devices are supported by Apple's built-in Airport service.

Download and try the macOS Lexmark Universal Mono Print Driver from that page. No guarantee it will work on Sequoia but all Lexmark offers at this late date. It would appear that driver was released in Spring 2024, and so was not specifically built for Sequoia, but probably your only hope.

Good find, Viking! The E342 driver page I found showed noting that new.