Might be up-castable to third level (if the spell can be upcast)
It is worth bearing in mind that the Monster Manual Variant Spellcasting for dragons is a DM option that lacks a great deal of specificity. The Monster Manual is a DM tool, strictly speaking, and the DM has considerable latitude in how to implement a dragon's spellcasting ability if it is chosen. A non-variant dragon does not have the Innate Spellcasting trait (thank you @Spitemaster)
Dragons as Innate Spellcasters (MM)
A young or older dragon can innately cast a number of Spells equal to its Charisma modifier. Each spell can be cast once per day, requiring no material Components, and the spell’s level can be no higher than one-third the dragon’s Challenge rating (rounded down).
Charisma Modifier: +4. Challenge Rating: 10 (young red dragon, MM)
This is a variant rule, so make a ruling (or propose one to your DM)
At first blush, casting the spell at its lowest level isn't a restriction. Since both of those spells can be up-cast per their spell text, and the dragon can cast spells at third level based on CR/3, the dragon could cast them at up to third level. Does the DM want to treat the dragon like a Warlock? There isn't guidance on that one way or the other, so the DM can treat all of this dragon's spells as third level spells.
But wait! Innate spell casting has a restriction
A monster with the innate ability to cast Spells has the Innate Spellcasting Special trait. Unless noted otherwise, an innate spell of 1st level or higher is always cast at its lowest possible level and can’t be cast at a higher level.
This text suggests that the invisibility spell would be cast at 2d level and could not be up cast.
Is there a loophole? Maybe. You can argue that there's a 'noted otherwise' in the dragon's variant ability and thus innate spellcasting is not a hard restriction.
the spell’s level can be no higher than one-third the dragon’s Challenge rating (rounded down)
The restriction is "no higher than." This can be looked at as specific over general (Basic Rules, p. 5) that opens an exception to the general rule since it only limits the dragon spell levels at the upper end. You can make the case (as Szega does) that this isn't specific enough to override the general innate spellcasting rule. (A fair ruling).
Variant Dragons aren't described as having spell slots
A monster can Cast a Spell from its list at a higher level if it has
the spell slot to do so. For example, a Drow Mage with the 3rd-level
Lightning Bolt spell can cast it as a 5th-level spell by using one of
its 5th-level Spell Slots.
That leaves open to DM ruling whether spell slots are even a thing for a dragon. If they are not, then dragons are only limited by their CR for the level at which their spells are cast. For example, are the spells cast as a warlock's spells are cast, all at the same level? That's up to the DM to decide.
"The spell’s level can be no higher than ..."
When a spellcaster casts a spell using a slot that is of a higher level than the spell, the spell assumes the higher level for that casting. For instance, if Umara casts Magic Missile using one of her 2nd-level slots, that Magic Missile is 2nd level. Effectively, the spell expands to fill the slot it is put into. (Spell casting, Chapter 10)
We begin to see how wide open this variant rule is. Most of the other spell casters (like the Archmage or the Cult Fanatic) have spell slots listed and depicted. The dragon doesn't. This all boils down to how the DM wants to treat the dragon's not having assigned spell slots. Is this a a restriction or not?
- If it is a restriction, go for the simple ruling.
- If not, go for the more nuanced ruling.
Simple ruling: can't be up cast.
Due to innate casting's general limitations, the simplest way to approach this is "the dragon casts spells at their lowest level." This is further supported by the lack of spell slots to assign to a given spell.
More nuanced ruling: yes they can be upcast
The specified restriction on spell level is based on the dragon's CR. The appeal to specific over general is that the text specific to the dragon only limits spells maximum level. A lower level spell cast at a higher level expands to fill the slot ... That's not strong argument, but it's a way to apply specific over general to a wide open variant rule.
And this is a dragon. Who is to say that their spell level doesn't work like a warlock's? The DM.
This is a variant rule, its application will need to be adjudicated by the DM.
What ruling is more fun at your table? Discuss with your DM.
It's a dragon - they named the game after these creatures.