Hi Rebecca,
You have been getting all very good advice to your problem here.
Firstly, you are using the wrong paper. Ilford papers are great papers and I use them a lot - but not for lith - they are not designed for it.
Paper choice is the first decision that will have a major, repeat major, effect on the appearance of the lith print. Not all B&W papers work well or at all, but many do. This will affect both the colour(s) you get and the tonality, graininess etc. If not sure what you want start with a paper well suited like Fotospeed Lith paper. There are many others (around 60 listed in the new book, but some are re-badges of course, but still a lot).
If you have a particular look in mind, this is the first choice to get what you want. If just trying it to feel your way, try an easy one and play. Or try 2 completely different ones to compare - e.g. Fotospeed Lith and say Foma Fomatone (RC version if you want). The latter is more colourful (especially in high dilutions) with a smoother look, and tones differently.
Your second choice is dilution. This can also have a major effect. Generally speaking higher dilutions give more colour, but papers vary in how much colour they will deliver. The Fomatone is very dilution-sensitive and gives an orangey pink shifting to salmon and can give colour splits too (a bit like split toning, without toning). You may not want salmon or maroon images of course - but they tone differently. They also have a different tonality even after changing colour in a toner. As well as more colour, higher dilutions tend to give a softer black (lower 'Dmax') and an extended tonal range in the light tones.
Adding old developer: Some papers give less colourful results (like B&W) in fresh lith dev. Adding some old to the fresh leapfrogs that stage. Some papers don't need it so much. You will get to know which do or don't (or which you prefer) by noting how much the colour changes through a printing session as the dev gets used.
These 2 factors have a big effect and people use which they like for their work. In the new book we have portfolios from someone who uses strong fresh developer for just 3 minutes, someone who uses very weak developer for up to 45 minutes - and someone who uses old nearly exhausted developer. Their results are all very different and each folio has a distinct personal look. (also work using additives or 2 bath techniques etc etc - so there are many variables but keep it simple to start with or you will get lost).
The process is actually easy to do. Pick an approriate paper, over expose a lot, control highlight density by increasing or decreasing exposure, control shadow density by pulling from the dev earlier or later.
Bob's comment about neg development is good too when you know the look you are after and want the neg only for lith. His prints are great. Someone else will want a different effect (viz my comments about the folios above) and will want a different type of neg. If you process negs negs normally you still have the option to print them any way you want and Lith is so flexible you can still get a huge range of results from one normal neg.
Above all, 1: keep it simple 2: change one thing at a time and keep notes 3: try a few very different paper types & 4: play. Having fun is the best way of learning.
Tim