Jones, who was also handed the honour in March, led the Owls to four wins and a draw from their five matches last month.
Defender Llera played a big part in that success, helping keep two clean sheets and scoring four goals as the club gained pole position in the race for automatic promotion ahead of city rivals Sheffield United.
Praising Llera, Jones told the Football League website: "Miguel has been outstanding throughout the month. He's played a key role at the back and also at the other end of the pitch where he has scored four valuable goals."
