According to the Dictionary of National Biography, Manners did not die on the Resolution during the battle, but some days later on the Andromache bound for England, having developed lockjaw (tetanus?) as a result of his wounds
Stothard, Thomas | Sherwin, J. K. | Sherwin, Charles.
London (no. 39 Fleet Street) : T. Macklin, August 15th 1786.
1 print : engraving ; platemark 49.2 x 61 cm
The death of Lord Robert Manners ... From the original picture painted by Stothard, in the possession of His Grace the Duke of Rutland. Engraved by J.K. Sherwin, Historical Engraver to His Majesty, & to His Royal Highness the Prince of Wales; and Charles Sherwin, Engraver to His Majesty