Due to firmware (updates) on most Lexmark printers, some won't recognize a refilled cartridge at first, but usually pressing "OK" or "RESUME" allows one to continue to print (even if you get a message that it is low or out of ink, which is not accurate). Unfortunately, Lexmark are not very friendly for refilling, but even for original brand, the issue rate is much higher than other models. If you have tried pressing "OK" or "RESUME" and you are physically still locked out from printing, please try this procedure:

http://images.lexmark.com/publications/pdfs/2007/3500/mhs/en/d0e10224.html

Or as a last case resort, get a piece of scotch tape and cover up the left column of contacts with the tape (the contacts are on the back of the cartridge, on the sensor strip). Put the cartridge back into the printer and try to print again. Taping the left column of contacts on the back of the cartridge (on the sensor) will fool the printer to accept the cartridges. 

This includes cartridges such as:
Lexmark 1 / 2 / 3/ 4 / 5/ / 14 / 15 / 16 / 17 / 20 / 25 / 26 / 27 / 28 / 29 / 31 / 32 / 33 / 35 / 36 / 37 / 40 / 41 / 42 / 43 / 44 / 50 / 60 / 65 / 70 / 75 / 80 / 82 / 83 / 85 / 90

(all of these models have sensors)