"Lloyd has been advised to withdraw from rugby for at least 3 months in order to fully rehab his neck," said Dragons Director of Rugby Robert Beale.
"We are obviously disappointed for Lloyd, particularly with the Six Nations coming up, but Lloyd's safety and welfare has to be paramount."
The retirement of Tom Willis and Burns' injury leaves the region with the trio of Steve Jones, Rhys Buckley and Sam Parry covering the position.
The Dragons head to Perpignan this weekend for a key battle in their fight for a knock-out place from the highly competitive Pool 4. They comfortably beat the Top 14 side at Rodney Parade, but then lost twice to Exeter Chiefs.
They need to complete the double over the French giants to stand any realistic hope of progressing in the tournament. They complete their Pool matches with a home tie against Cavalieri Prato next weekend.