Growing from a very small size to an extremely large size is no problem, as dinosaurs show (and remember, ultimately even the largest dinosaur started as a single cell; the size of the egg is basically about how much initial nutrients are stored for the organism until it is ready to get out of the egg).
I don't think you could get literally to mountain size, but if taking that as hyperbole, I'd say that 12 meters of length for T. Rex is already a very impressive size (and at least in the fantasy with dragons I've read, which admittedly is not very much, the dragons weren't much larger).
Now flying could be a problem with large sizes. However a Quetzalcoatlus was still of impressive size. Bat-like wings should probably not be a problem. Whether a lizard-like appearance would be realistic probably depends on how exactly you define "lizard-like". There would probably be some shape requirements for aerodynamic reasons. But otherwise I see no reason why this should not be possible.
The most problematic point, of course, is breathing fire. As far as I know, there's no known animal that does or did that. However, we know that inflammable substances can be produced by organisms (those include both alcohol and methane; indeed, the latter is commonly produced in the intestines of all animals, thus it is not that far fetched that dragons might be able to burp it out on purpose), and we know that in principle it should be possible to safely emit fire (every fire-eater shows this). The main problem would be how to ignite the breath (in a way not to harm the dragon itself). However, I guess that should be a solvable problem; there could be for example some substances which the dragon could emit in small amount together with the inflammable gas or aerosol, which has a strong exothermic reaction in air, thus igniting the gas. Maybe there's a chemist here to tell whether that would be possible/feasible. Another possibility would be some spark-generating mechanism in the mouth; maybe the dragon has evolved special teeth with flintstone-like properties.
Another consideration is that a substance that easily inflames in air would be hard to contain, and thus very unlikely to evolve, therefore a better solution would be a two-component ignition, where each substance in isolation is harmless, but when they meet they ignite. If the substances have a use also in isolation, this is more likely to evolve, and it is not unrealistic that at some time a mutation caused them to be emitted at the same time, giving the ability to breathe fire.