Let's first establish the basics. "Mercenary" is usually used to mean "a soldier who fights for money". Sometimes people will agree to be soldiers for some nation or cause, not because they are patriots who believe that this cause is noble or just and worth risking their lives for, but because they are paid a lot of money. More generally, "mercenary" can mean someone who is only interested in money, or as an adjective it can mean an excessive desire for money.
Here, "she" (whoever she is) wanted to give Home money, but he tried to convince her to give the money to her relatives instead. That is, Home did NOT have an excessive desire for money. He didn't want the money at all.
So the writer says "a less mercenary man never lived", that is, there is no one who cared less about money than Home. He didn't care about money at all. If you looked for someone who cared about money less than Home did, you wouldn't be able to find such a person.
This is a fairly common idiom. Not specifically with the word "mercenary", but using any adjective, and using "less" or "more" as appropriate. "A more humble man never lived ..." "A less ugly man never lived ..." etc.