I doubt he’s lying. I think staff came up with the list and stuck it under his nose and he signed it as he was packing up his office. I don’t think he knows who decided on the list abd given what was going on he probably didn’t care then and doesn’t now either
The list was for his Operation Warp Speed team so it wasn’t some obscure group of people that his staff cobbled together for a last minute stack of papers.
http://trumpwhitehouse.archives.gov/briefings-statements/remarks-president-trump-operation-warp-speed-vaccine-summit/ (at the summit on Dec. 8.2020, Presidential Commendations awarded Jan. 19, 2021)