Try applying a warm compress to the eye to see if the lump will soften. If it's pus, then it's unlikely you will get it out with a needle. Chicken pus is a semi-solid type of material.
Looks like it may be sinus or respiratory infection.
Clean the eye with saline, press the lump to see if you can push any pus out.
If you have something like eye ointment, you can put that in the eye too.
Be sure to look inside her beak for any lesions or canker.