lookup field optional
1) On the Page Layout itself, a field can be made "Required". Check the Page Layout.
2) If the Lookup is a "Master-Detail" lookup, then I believe it would be required. Have a look if the field is a standard "Lookup", or "Master-Detail".
3) A Validation Rule could be written to require a field value. You'd know if this was happening, if you get a very specific error message when trying to save the record with no lookup value. But you could check Validation Rules on the object nonetheless.
I hope this helps! Good luck!