There are a million different ways LDs get hired. Most of the 'big name' work for a design firm or have their own company. Some examples:
Roy Bennett,
Baz Halpin,
Spike Brant's . This heavy hitters will have an agent or manager working on their behalf to handle the business side of things. It also lets them have a team that is working with them not competing against them. If they are booked on another gig when a repeat client needs them they are able to keep the work in
house rather than let a competitor steal it. Other LD's have a more informal approach.
Hiring an LD or a firm can be done by the tour's
production manager, the artiste's management, the vendor or the record label. It depends on the size and scope of the tour. An openign act might tip out one of the lighting guys from the
headliner to run lights for their set. A small
headliner might ask the lighting vendor for a suggestion. But the bigger tours know who they want based on style and price.