The pair are in a share of 22nd position after rounds of 67 at the Chitimacha Louisiana Open to be five shots of the pace set by Nate Lashley who was a three time winner on the Latinoamerica Tour in 2016.
Allenby no longer has PGA Tour status and is now playing the Web.Com Tour as he chases a return to the PGA Tour which he has played since 1999 while South Australian Lutterus, also a former PGA Tour player, Monday qualified for this week's event.
Steven Allan is next best in 34th place after his opening round of 68, while Peter Lonard and Jamie Arnold opened with rounds of 69
Rhein Gibson and Nic Cullen are further back after rounds of 73 and 74 respectively.
Want video tips delivered straight to your inbox? Subscribe to iseekgolf.com newsletters.