Lily just wanted lower prices for her drugs, not starting a war but indeed I don't buy the mastermind girl persona DPC is trying to sell. The way Lily switched suppliers was stupid. Her excuses for not buying drugs from Vinnie wouldn't have fooled a half brain dimwit and instantly buying from another dealer selling the exact same product was even more stupid. Even the way she immediately came to Quinn's rescue when Vinnie arrived in Episode 9 was suss. It was litteraly admitting to Vinnie she knew about Quinn being a dealer too and that they were acquainted. It was almost a direct confession.
A smart girl would have waited a couple of weeks before buying from another seller and started small so it wouldn't have aroused suspicion but aparently Lily is supposed to be one of the smartest character of the game, that's probably why the bar is not very high.