He has a chicken that lays golden eggs!
Joke aside, the first thing we have to remember is that Zaun is practically run by mega corporations. The government has no real power. Another very important thing is that when Pididly stole Blitzcrank, Viktor's pleas were ignored by the grand court; which is strongly tied to the government as the second of three institutions that "rule the country". I don't think Viktor would be too eager to ask for funds from the institution that wronged him.
On the other hand, with the corporations being so influential, it is possible that some of them are commissioning him to create better industrial equipment and machines. He is after all a scientist, he surely knows how to create something other than augments. And not all companies would want just augments. They're all competing in production and Viktor is probably one of the most innovative creators in Zaun.
He's surely receiving donations from people who believe in his cause, but I imagine that being less than what he probably gets from Zaun's corporations. The corporations don't care who they fund, as long as it's benefiting their development.
The last point, which perhaps belongs at the beginning, is the fact that when he began his transformation, he already had a private laboratory. Not only that, but he attended a prestigious college, and I believe everything in Zaun must be payed for. Perhaps he was from a better standing family.
Viktor generally acts as a secluded person, and even though he may be viewed as an outcast in Zaun, Piltover's government couldn't have known about that. They probably didn't want to risk attacking a person that might be very important to Zaunites.