Nigel Lindsay so-starred with David in the 2003 world premiere of the play The Pillowman, David played the storyteller Katurian and Nigel played one of the policemen who interrogates him called Ariel. This is a picture of them from the production. (photo by Ivan Kyncl)
In 2011 Nigel was cast in the lead of Shrek The Musical as we all know Shrek has a Scottish accent, to help him prepare he asked his friend David to help:
“It is a hell of a part. [The producer] Caro Newling said to me, 'It’s like the King Lear of musicals.’ They told me that, for this, they saw a lot of actors who can sing, rather than musical actors, because the make-up and padding are so thick, you need to see a bit of humanity come through.” Vocally, they may also hear a touch of Time Lord. “I phoned David Tennant, who is a mate, and said, 'I want to do a hybrid of you and Kenny Dalglish. He said, 'If you do Kenny no one will understand it.’ I said, 'Yeah but you’re too fey.’ He said, 'I’ll butch up for you.’ I went round to his place and he read a bit of the script for me.” - The Telegraph - May 4, 2011 - Jasper Rees
Here's Nigel as Shrek -