Limehouse Lizzy guitar player Greg Alcock woke up to find the band's new Mercedes van missing from outside his home in Park Lane, Rothwell.
All the band's equipment - from guitars, amplifiers, a mixing desk and a huge backdrop with the band name in lights - were inside.
Greg said his 'heart sank' when he realised what has happened - but now insists 'the show must go on'.
He formed the act in 1993 with Wayne Ellis - who performs as the legendary Phil Lynott - and they have been hailed as one of the UK's hardest working tribute acts by the Performing Rights Society.
The band settled in West Yorkshire after gaining a following at some of the region's best venues - including the now-closed Duchess of York in Vicar Lane and the Brudenell Social Club.
Greg said they'd had an 'unbelievable' amount of support from the Yorkshire music scene since the theft, which happened between Wednesday night and Thursday morning.
"We've had people offering us guitars, amps, everything," Greg said. "Now we are just trying to piece things together for the shows for the weekend."
The band had to cancel Thursday night's show in Swindon, but plan to perform in Colchester and Portsmouth on Friday and Saturday.
"I think they wanted the van," Greg, who was a guitar technician for the real Thin Lizzy and has performed with members of the band, said.
"I think the gear itself will be a hot potato. The huge mirrored backdrop has the band name in lights - who is else is going to use that?"
The timing has been particularly cruel, as the band has been increasing the size of its production as they are playing 'bigger and better' shows.
The van had been specially adapted to go on tour, with space for all the instruments and crew on board. They have a run of festival and European dates over summer.
"It's not just about us though," Greg added. "The live music scene is on its knees. Venues can't afford to shut their doors for a night, not pull any pints and refund tickets."
He has contacted Leeds music shops to keep an eye out in case their equipment shows up and is calling on anyone with information to contact police.
The van is a white Mercedes Sprinter with the vehicle registration YH65 UDN.