In the context of Market making, how important is recent trades? In general, would i be able to get away with just modelling the Limit Order Book (LOB) and the evolution of the LOB in order to decipher a 'fair price'?
By "modelling the LOB and the evolution of the LOB" you are modelling trades by definition as they are what determine how the LOB is going to behave.
The evolution of the limit order book is dependent on both the internal dynamics of the book for current pending orders (e.g., if there are a bunch of limit orders to sell at price $X$) as well as recent trades. As a market maker your job is to quickly adapt to theses changes in the books in order to provide actual liquidity (i.e., not orders with spreads way out of whack of what the asset is currently trading at).
Trades are obviously very important.
At the elementary level, a market exists for the purpose of matching buyers and sellers and the mechanism adopted to establish price discovery in LOB is to have liquidity providers display passive orders on the book while liquidity takers lift it by crossing the spread.
Ignoring trades is ignoring the essential and basic process by which price formation occurs.
It goes without saying that any market maker who would decide to ignore trades would be doomed.
In my experience, this is not as black and white as some of the answers would have you believe.
From a feature engineering POV, I've seen some markets where trade related ML features are dominant and some markets where LOB features dominate.
However, just modelling one without the other would likely be a mistake.