wrote:
I have refilled various inkjet cartridges(HP, Lexmark) to varying
degrees of success. After I reinsert the cartridge, I always get the
low ink message when I try to print. Has anyone figured out how to
reset the printer so it reads the new ink levels?

You're not trying very much to help yourself out. Some answers have
been around for years. Google has answers. This group's archives have
answers. The refill sites have answers. Experimenting would reveal
answers.
Depending on the cart #, there are ways to tape off certain contacts
on the cart and have the printer initialize it as a new cart. Also,
cycling multiple carts in and out will cause the printer to recognize
the next cart in as new. What to do depends on what you have and it
might not work on some newer models.