The Gatherer page for Fires of Invention says (emphasis mine):
You may choose to pay the mana cost or an alternative cost for spells you cast, even if their converted mana cost is less than or equal to the number of lands you control.
as well as
If you cast a card “without paying its mana cost,” you can’t choose to cast it for any alternative costs. You can, however, pay additional costs. If the card has any mandatory additional costs (such as that of Fling), you must pay those to cast the card.
So yes, you can cast an overloaded Mortars, but the Fires will not help you to pay for it.
Both "without paying mana cost" and "Overload" are alternative costs, and when you cast a spell, you can only choose 1 alternative cost to use. So you can either cast Mizzium Mortars for free, or you can cast it by paying its Overload cost and getting the Overload benefit. But you can't do both.
118.9. Some spells have alternative costs. An alternative cost is a cost listed in a spell’s text, or applied to it from another effect, that its controller may pay rather than paying the spell’s mana cost. Alternative costs are usually phrased, “You may [action] rather than pay [this object’s] mana cost,” or “You may cast [this object] without paying its mana cost.” Note that some alternative costs are listed in keywords; see rule 702.
702.95a Overload is a keyword that represents two static abilities that function while the spell with overload is on the stack. Overload [cost] means “You may choose to pay [cost] rather than pay this spell’s mana cost” and “If you chose to pay this spell’s overload cost, change its text by replacing all instances of the word ‘target’ with the word ‘each.’” Casting a spell using its overload ability follows the rules for paying alternative costs in rules 601.2b and 601.2f–h.
118.9a Only one alternative cost can be applied to any one spell as it’s being cast. The controller of the spell announces their intentions to pay that cost as described in rule 601.2b.