"We don't pretend to be him," said the group's Bruno Bouchard. "The only tribute would be to honour his work by playing it. It's just like playing the Shakespeare texts. You don't tribute Shakespeare. You play Shakespeare. So that is kind of the way we get into this whole world."
The name of the outfit, which performed at the New Zealand Festival in Wellington before playing three nights at Auckland's Q Theatre, translates to "a band of one-man bands". They're part band, part arts collective.
The Waits show is but one project involving LODHO combining live playing and theatre to make "music to be seen".
"The company is a multi-disciplinary art company so we're very much into music but we are very influenced by visual art, poetry, performance, theatre and dance."
It was Waits' sometimes abstract music which inspired the mixed-up approach. "His music has a lot of texture - texture in the voice, texture in the percussion and all that and trying to find how to reproduce or go into that sound, we discovered how to play music with objects.
"That became a way of doing music that we brought to other shows.
"In our show it's not that we play Tom Waits, it's we somehow play at Tom Waits.
"The idea is that we take the rules he was playing music with and we try to play music with those rules but in our own way. So sometimes we transform his music into some other kind of music, being really respectful to the melody, to the harmony.
"People are going to recognise the songs ... but it's something that comes from his world and ours at the same time."
They have been playing the Waits show for six years now, complete with a mix of traditional instruments and invented ones, as well as kitchen implements, tools, and some other stuff that can make international touring interesting when it comes to customs halls. Anything to declare sir?
"Well I have a cow skull and spaghetti," laughs Bouchard "I make music with it but, listen, it will be hard to explain."
Waits has apparently heard of LODHO's take on his music. But if the man himself turned up to a gig, Bouchard isn't sure what his reaction would be.
"Maybe we could let him sell his CDs at the door."
What: L'orchestre d'hommes-orchestres
Where: Q Theatre
When: Tonight 7pm, tomorrow and Thursday, 8pm