Thank you for the prompt reply.
Without being able to examine him, it is difficult to know what is causing the lump. Of course a tumorous mass is a possibility, but there are others. The roots of the chewing teeth are deep in the jaw and if a dog develops a root tip abscess, it can lead to a large swelling and even effect the eye if the infection is bad enough. These will sometimes even rupture open and there can be a pus drainage. It is possible that may be what is going on. Unfortunately, there is not much that you can offer without veterinary intervention.
It is best to keep any discharge from building up around his eyes by wiping gently with a warm water cloth. You can try flushing his eyes with eyewash or saline solution (like contact wearers use). He may also get some relief from an artificial tear type solution applied as frequently as needed to keep the eyes lubricated. The product called Genteal® is available over the counter (OTC) as a solution or a gel.
You can also try to apply cool compresses to the lump as it may provide some relief. If this is an abscess, it is best to have the affected tooth extracted, but antibiotics will be needed as well.
I hope this is helpful. Please let me know if you have ANY other questions. My goal is to give you 100% satisfaction and if you are not yet satisfied, please reply so I can clarify for you.
My posted replies are for general education only and not meant as a diagnosis. Only after a thorough veterinary examination can a diagnosis for your pet be made and specific treatments be advised or medications be prescribed.