If you want to keep using the same bath, then replenish it. I don't know what developer you are using or in what concentration so I will use my developer/dilution as an example.
I use Fotospeed LD20. Initial dilution is 100ml A + 100ml B + 3800ml water + 100ml old brown in a 16x20 tray. When the colour of the print goes beyond what I want (usually around print 15), I replenish with 100ml A + 100ml B + 50ml sodium sulphite (that's sulfite with a "t"). I make the replenishing solution up in advance in a 2 liter container. I fill this bottle up with used developer from the tray for better mixing; then pour the whole 2 liters back into the tray. Sometimes I replenish with less than the above formula but in the same proportions. The next few prints will resemble the earlier prints from the fresh bath. I eventually get back to the colour I want. At that point I process 2 or more prints at the same time for consistency. This assumes I want multiple copies.
Another use for old lith developer is as a second-pass lith. Bleach to completion, or a portion thereof, a print processed in a regular developer. Process the bleached print in the old lith developer. As Mark says, it works better heated to around 40 degree Celsius. Warmtone papers such as Ilford Warmtone work well with this process.