With helpful advice and encouragement from fellow Ravelry members, I decided to try freeing up the pattern drums.
First I took off the plastic cover. Then I squirted lots of surgical spirit over the drums. I put a few drops of oil onto the moving parts, but to no avail, so back to Ravelry for more hints and tips.
Ozlorna advised using a hair-dryer to loosen up the old gunky oil.
I alternated between squirting with the spirits and blowing with the hair-dryer and eventually the drums began to turn. After about 2.5 days things began to move pretty well.
I have just tried the carriage out and lo and behold, it works!
I just did a swatch to try it out and here is the result;
I am very pleased with the result. I over-killed it with the steam in my haste to show off, but I now feel confident that I can now knit something wonderful with my lace carriage. Happy Knitting.