The visitors were leading 8-5 early in the second half when forward Cooke was forced off with a shoulder injury.
The blindside flanker had been a key figure in the Lions lineout and once he’d gone off, they struggled to exert the same measure of control.
Interim head coach Gregor Dougall admitted the loss of Cooke was probably the game’s pivotal moment.
The defeat left them still in the bottom three and Dougall said: “The game was tight and it all turned when we lost Sam.
“He was fantastic in the lineout for us, especially on their throw but all of a sudden we weren’t winning their ball or our own. We did not help ourselves by picking up two yellow cards but our defence, particularly when we were down to 13, was outstanding.”
Beckenham dominated possession in the first half but found points at a premium.
They made the breakthrough from a set piece but Matt Halpin’s penalty for Lions meant only two points separated the sides at half-time.
Deal-Bettes made an excellent start to the second half with Luke Armstrong picking up a loose ball in his own half before racing over but the loss of Cooke came soon after.
Beckenham swiftly pounced for their first try and later added a second although they failed to score at all while Lions were temporarily down to 13 through the two yellow cards, which came within minutes of each other in the final
quarter.
Jonathan Stabler played 80 minutes after a break of several months and was joined by fellow returning lock Dan Atkinson.
The losing-bonus point Lions collected proved enough to keep them just ahead of fellow strugglers Bromley, who won 31-18 against Heathfield & Waldron, who are also in the relegation mix.