ut mentiar, nullius patrimonium tanti facio

The purpose of this exaggerated statement of Niceros is to convince his fellow diners that he could not possibly be lying.

patrimonium: A patrimonium is property, including possessions, estates and money, which belongs to the paterfamilias. By extension it also means inheritance. The point of using this noun here is to refer to a large quantity of wealth.

Petronius has already used this noun with a similar sense in section 44:
plus in die nummorum accipit, quam alter patrimonium habet
(he receives more money in a day than another man has in inherited property)

facio: The verb facio can have the sense of to regard/consider/treat something (as). [OLD 18b] When used in conjunction with the genitive case it can mean to esteem or value (at). [OLD 18c]

nullius tanti: Genitives of quality which denote indefinite value.

ut mentiar: A result clause, indicated by tanti.

In English one might say the similar sentiment of, “I wouldn’t lie for all the money in the world.”