Pretty much just what the title says. Would it just starve and die over time, or would it be able to survive in some way?
I’m assuming a red dragon, and the lair being something in line with the description in the MM: "Red dragons lair in high mountains or hills … Caves with volcanic or geothermal activity…"
So something in line with this, a cave in some high mountains.
For this case, I am assuming the standard rules (not the spellcasting variant).