The rule states that halfling luck applies to saving throws and the death rolls are called "death saving throws." Based on that I decided to allow it. Additionally, I thought allowing halfling luck on death saving throws was also within the spirit of the game. I've been unable to find anything in the rule books that addresses it.
\$\begingroup\$ Related: What ways (other than advantage) are there to improve the total for a death saving throw?, How else can I get Advantage on Death Saving Throws?, Do Bane/Bless apply to death saving throws?, Does a Paladin's Aura of Protection Affect Allies' Death Saving Throws? \$\endgroup\$– V2Blast ♦Nov 4, 2020 at 1:51
Yes, the Halfling racial feature Lucky works with death saving throws.
Whenever you start your turn with 0 hit points, you must make a special saving throw, called a death saving throw, to determine whether you creep closer to death or hang onto life. Unlike other saving throws, this one isn’t tied to any ability score. You are in the hands of fate now, aided only by spells and features that improve your chances of succeeding on a saving throw.
Lucky is exactly this, a feature that improves your chances of succeeding on a saving throw.
Even ignoring this (reasonably explicit) statement, a death saving throw is "a special saving throw" - it's pretty clearly a saving throw, and Lucky says that it works on saving throws.
\$\begingroup\$ A death saving throw is a saving throw is a saving throw. My divination wizard will have to remember this as well. \$\endgroup\$ Apr 19, 2016 at 16:58