I just finished clearing 8 severely plugged grease lines on a 5 axis router. I used a grease gun that I made a new tube and end cap (sealed) to pump cleaning solvent into the lines to liquefy the grease. After that, 5 of the 8 were clear.
The following 3 that were more stubborn needed a lot longer to break down the grease. I took some small air cylinders and plumbed them into the clogged lines. I filled the air cylinder pressure side with solvent and then connected the other side to shop air. It took about 3 days of this constant (low 120 psi) pressure on the solvent to finally loosen things up.
I was very conservative with my pressure, because the last thing I wanted was to rupture a plastic line in a place that was not accessible. I was told to keep pressure below 200psi on the line I was using.
After you get the solvent to go through, be sure to evacuate any remaining solvent with plenty of new grease.
I used solvent tank solvent, as I knew it wouldn't hurt any of the seals that it might come into contact with. Don't use lacquer thinner or the like.
Be patient and you'll get it.
Mike