>>4477536
Basically what these guys said
>>4477563
>>4477592
Sometimes you can run the cleaning cycle to unclog and do alcohol swabbing if that doesn't fix it. The Lexmark manual says to wet a lint free cloth with water and swipe the print heads with it and then run the cleaning cycle. This doesn't always work from my experience with inkjets which is why I like the printers with heads built in the cartridges from a maintenance perspective.
You can also buy high quality inks like Lucia or Claria etc to refill but I would not recommend it. Just get a new cartridge, allegedly OEM for $16 on Amazon so not expensive imo although that's an old printer so the third party stuff might be better simply by being newer. Tank printers, like the Ecotank, and as cANON pointed out, most Epson printers, have separate heads but they aren't user-replaceable so if it gets really clogged you gotta buy a new printer. My Canon does have a replaceable print head but it's more than half the cost of the printer.
>>4477613
Think of printing every week or maybe even every two weeks as part of the maintenance schedule. You can bring it back to life with a new cartridge fairly cheaply, less than $20, but might as well get your money's worth from the ink you have even if you think a photo isn't worth printing - you can still learn "hmm, this photo doesn't look good in this dim room, maybe I'll mess with curves to brighten it" or "the shadows have a color cast that isn't visible on the computer, let me fix that" etc. You have photo paper for that Lexmark I'm assuming.
The used Ecotank I would ask for a sample print to make sure it isn't clogged and pass if it is just because you can't guarantee that cleaning the print heads / doing a cleaning cycle will fix it but could be a great bargain if it is working. You could gamble on being able to fix it if the price is good enough and the seller won't let you try.