If it's very stuck and grimy I would probably start with spray can oil, most of the brands work well as solvents and cleaners. I usually start by brushing out dust and lint, then oil with basic sewing machine oil and gradually amp it up from there. In stubborn cases you might start with more efficient solvents to begin with, like the various spray can oils most of us have or have had at some point. Alcohol works too. There's lots of different speciality products available, but choose something that will not harm the plastic in your Lydia. This model often needs some clever work arounds with a couple of parts that's often broken, but it has some nice stretchy stitches and simple design. Getting thick lumps of old grease usually requires lots of cotton swabs, tooth picks, cotton rags soaked in solvet... It usually comes off with out too much work.