Four tries in the opening 32 minutes of the game in Sydney ultimately proved the difference as England put themselves on course to finish in second place in Group A, with France still to come next weekend.
The team's early pressure finally paid off in the ninth minute when Kallum Watkins went over in the corner, with Gareth Widdop adding an extra two points, but Lebanon soon showed that they were keen to impress on the biggest stage.
After a grubber kick beyond a group of England players, Nick Kassis reacted quickest to touch down, with the scoreline being levelled up with the conversion.
England knew that they were in a game and it led to a strong showing for the remainder of the half, with Jermaine McGillvary going over the line after 24 minutes.
A third try through Ryan Hall arrived soon afterwards, although it was debatable whether he had full control of the ball, but England continued to build a lead with Ben Currie going over on the left after being given space to cruise over the line.
England had built a 22-6 advantage by the break and there was every expectation that Bennett's men would kick on after the break, but the game soon became an increasingly scrappy affair.
The next try did not arrive until the 55th minute when Tom Burgess side-stepped a Lebanon player before driving through towards the posts to give Widdop the chance to convert.
England would have had hopes of piling on the points during the latter stages but rather than tire, Lebanon enjoyed their best phase of the game as they looked to reach double figures.
Lebanon got their reward with five minutes remaining through Jason Wehbe, who powered over in the corner despite the attentions of a number of England players.
With the final kick of the game, Widdop added a drop goal but England will head into their final game of the group knowing that improvements need to be made if they are to make any lasting impression on this tournament.