I would like to add some things.
First, the asteroid belt is one of the least accurately depicted things in sci-fi. Star Wars, Star Trek and many other more or less popular stories show an asteroid belt as a region of space dense with large rocks frequently colliding with each other. There is an excellent answer about the density, or actually the sparsity, of our Solar System's Main Asteroid Belt: https://space.stackexchange.com/a/1388/47491. While some other star systems might have densely packed asteroid belt, I believe our Main Asteroid Belt is an example of a typical asteroid belt.
I have seen only two sci-fi stories somewhat accurately depicting an asteroid belt. First is 2001: Space Odyssey, where one very distant asteroid crosses the screen in one of the scenes of the two-hour movie. The second is The Expanse. In the books where the story is set around the Main Asteroid Belt, Jupiter and Saturn, the action takes place at particular asteroids and space stations: Ceres, Eros, the asteroid at which the Canterbury gets ambushed and destroyed, asteroid on which the Rocinante crew finds a stealth ship hidden by Julie Mao, Tycho Station, Toth Station...
In reality, when travelling in space, the only indication you are in the asteroid belt would be your ship's radar detecting asteroids and navigational computer comparing them with previously established maps.
Second thing, The Expanse also shows how space pirates would operate: lay in ambush relatively close to their prey's predictable route, hiding behind an asteroid or so close to one that radar have difficulty in distinguishing ship and asteroid, with the drive off, transponder off, active sensors off and only passive sensors on, and reducing heat radiated out into space, and some kind of bait in a trap. And when the prey is in the trap, then take action.
Third thing. Something else you have to consider, in addition to what's described in other answers, is the intensity of space traffic.
How many people are in your Universe, and how are they distributed?
Are humans (currently) the only spacefaring civilisation? If so, are they only living on Earth and occasionally sending some scientific probe out into space? Are they mining asteroids? Do they have permanent settlements on Mars? Are they living on every planet, moon and significantly large asteroid in our Solar System? Do they inhabit nearby stars? Galaxy(-ies)?
Or are there other spacefaring civilisations as well? Are there less advanced civilisations too? Has it led to colonialism? Do colonised societies fight for freedom? (Which would be cause for moving military around.)
How many people are travelling in space or working in shipping commodities around? What cargo is transported from where to where? What are distances and speeds?
What cargo would pirates be interested in, in terms of value, probability of getting caught by a law enforcement agency, and how easy would it be to sell it on the black market?
Is traffic organised? How? For what reasons? Who is doing it?
Is there a traffic control authority you have to submit your flight plan before your travel? Are they following whether or not you actually fly the route you submitted your flight plan for? How? AI-controlled observatories tracking spaceships in real time and comparing with submitted flight plans? Maybe regulations force shipbuilders to build in systems for automatic sharing of navigation data with traffic control authorities and other ships in reasonable vicinity?
Perhaps on less frequently travelled routes with a high probability of pirate ambush, cargo ships travel in groups escorted by the military?
In conclusion, considering different aspects and scenarios, it is plausible that shipping lanes of some kind in space would make sense.