Lynn’s neck surgery, which was due to take place before Le Mans, has been rescheduled and means he will not be able to take part in the French endurance classic.
Deletraz, who races full-time in IMSA for another Cadillac factory team, Wayne Taylor Racing, will once again join Norman Nato and Will Stevens in the #12 JOTA-run Cadillac.
The trio finished ninth at Spa after leading in the early laps of the race in the first couple of hours. But they fell back in the second half of the race to finish ninth.
"It's obviously hugely disappointing not to be racing at Le Mans and to miss the Silverstone test with the team, but getting this procedure completed and fully recovering has to be the priority,” said Lynn.
"The timing hasn't worked out as originally planned due to scheduling difficulties around the surgery, but we now have a clear path forward.
"I'll be supporting the team from home and I wish Louis, the #12 crew and everyone at Cadillac Hertz Team JOTA the very best for Le Mans."