| Luagsharpshank |
There is a way in Pathfinder for an alchemist to turn lead into gold, but it requires the character to be a 20th level alchemist and choose the philosopher's stone grand discovery. Turning lead into gold was supposed to be the ultimate achievement of an alchemist. Making it a capstone of the class is entirely appropriate. This is not something a low or even mid-level character should be able to do.
As I pointed out in my first post you can use craft alchemy or any other craft or profession to make money, but it will not going to instantly make you wealthy. Doing so is not going to be turning lead into gold; it will be creating alchemical items, or maybe making potions.
The 20th level grand discovery does not just permit the transmutation of lead into gold. It permits the creation of the philosopher's stone minor artifact:
https://www.d20pfsrd.com/magic-items/artifacts/minor-artifacts/philosopher- s-stone
Which can create 50,000 gp in transmuted gold (minus the cost of 1,000 pounds of lead) or just a level 9 cleric true resurrection without the 25k material component.
They get one of these every month at no cost. Of course at level 20 gold is trivial, so this GRAND DISCOVERY CAPSTONE is actually not that big of a deal.
Now that all that is out of the way, there is no reason an alchemist might not be struggling to transmute minute amounts of gold all through their careers, and it is very in keeping with the fantasy that alchemists be given royal patronage to transmute base metals to gold.
Coming around to RAW: The Craft skill lists "Practice a Trade" as a use of the skill where you earn half your skill check in gold a week. There's no reason a GM could interpret that to be actually "making" half your check in gold a week. Pump your skill and make a little gold in a cool alchemic way. I certainly think there are more efficient ways to earn money, but that's neither here nor there.