Is it serious to have a pea sized lump on the outer part of the vaginal lip? It itches and after a few days I squeezed it and brown pus came out.

No. This is a very common occurrence, which is simply an inclusion or sebaceous cyst and what came out was not pus but sebum, like a whitehead on your face. See these all the time in my clinic. Can drain or excise them if desired for cosmetic or comfort reasons but no risk in leaving them alone.
Cyst. Probably its a follicular or hair follicle cyst if its on the ouside of the lip. If on the inner lip it may be a gland issue. You can also get vulvar mucocoeles. All are benign issues. However, its always a good idea to have someone look at it.