"In the market" or "on the market"

I am trying to help a friend of mine proofreading an English email and she has a preposition there that I am not completely certain is correct. The original sentence was this:

[Name of the competitor] had the lowest price in the market -- [the price].

This seems a bit odd to me, but I can not be completely sure if I am right about the proper usage.

My intuition wants to say "on the market" at this point...

Your intuition is correct. The sentence should be:

{Name of the competitor} had the lowest price on the market...

Usage is idiomatic. "The market" isn't referring to a physical marketplace such as an open-air fish market, or a farmer's market. Instead, it is an abstraction, like an economic market, and may refer to automobiles or housing.

Usage is slightly different if the market is financial, such as a stock or commodities market.

• Buying and selling of stocks refers to "the stock market". A particular, but still abstract, instance is "the European stock market".
• A named market is a proper noun, often a physical entity, such as the Paris Bourse or the London Metals Exchange (LME). Virtual markets are markets too. The NASDAQ is an all-electronic exchange. Bitcoin is too.
• "Commodity" is used as an adjective to describe the type of market e.g. platinum options are traded on a commodities market such as the Chicago Mercantile Exchange (CME) or the LME.

Pork bellies are traded on an agricultural exchange (market). Pork belly futures are listed by, or on, the CME. The traders themselves are in the market to buy or sell pork bellies. That is metaphorical too. It doesn't describe location, but rather, intent to act. If the traders were on the market, then the traders themselves would be bought or sold! Very meta, to trade traders, and wrong, as traders aren't chattel.

Summary

One takes one's pigs to market, sells them in the marketplace, offers them as listed futures on a commodities exchange, and sells them to the highest bidder on the market.

Generally speaking, only the commodity itself is on the market, while the traders themselves and other aspects of the trade are in the market. So one puts one’s pork bellies on the market at the lowest price in the market.

in the market : in the position of being a potential buyer <in the market for a house>
on the market : available for purchase; also : up for sale <put their house on the market>¹