Simon Murray scored a double, while Fraser Murray and a Brian Graham penalty secured the win.
"The squad is thin so we need to bring two or three in," said head coach Lennon. "It's a slow process sometimes, but we'll see what this week brings."
In the other Group D game, Ross County were 2-0 winners over Alloa Athletic.
Marcus Fraser and Craig Curran scored either side of half-time for the Premiership side, who host Hibs on Friday night, against their League One visitors.
Hibs had announced the signing of Steven Whittaker before kick-off, but the former Norwich City right-back was not registered to face their League Two visitors.
"We were without him, Efe Ambrose, Paul Hanlon and we gave Marvin Bartley a break, so we're very strong at the minute," said Lennon, who says an additional striker is now his priority.
Hibs are preparing for their return to the top flight and Lennon said he "got everything that I wanted from my players".
"It was excellent considering where we are in terms of our start to the season," he added.
"It was a good game for them in terms of working on their fitness going forward.
"Even though it was a competitive game, in my mind it was a pre-season game.
"We weren't going to learn much from it, but the important thing was to get the win and win well.
"The lads will get the benefit from the game today."
Match ends, Hibernian 4, Montrose 0.
Second Half ends, Hibernian 4, Montrose 0.
Corner,  Hibernian. Conceded by Craig Johnston.
Corner,  Hibernian. Conceded by Graham Webster.
Goal!  Hibernian 4, Montrose 0. Brian Graham (Hibernian) converts the penalty with a right footed shot to the bottom left corner.
Penalty conceded by Graham Webster (Montrose) with a hand ball in the penalty area.
Attempt missed. Oli Shaw (Hibernian) right footed shot from the left side of the box misses to the right.
Attempt missed. Graham Webster (Montrose) header from the right side of the six yard box is close, but misses to the right following a corner.
Corner,  Montrose. Conceded by Ryan Porteous.
Foul by Ryan Porteous (Hibernian).
Craig Johnston (Montrose) wins a free kick in the defensive half.
Attempt missed. John McGinn (Hibernian) left footed shot from outside the box is too high.
Kieran Thomson (Montrose) is shown the yellow card.
Dylan McGeouch (Hibernian) wins a free kick in the defensive half.
Foul by Kieran Thomson (Montrose).
Fraser Murray (Hibernian) wins a free kick in the defensive half.
Foul by Liam Callaghan (Montrose).
Substitution, Hibernian. Oli Shaw replaces Simon Murray.
Attempt missed. Brian Graham (Hibernian) header from the right side of the six yard box is close, but misses to the right.
Foul by Ryan Porteous (Hibernian).
Craig Johnston (Montrose) wins a free kick on the left wing.
David Gray (Hibernian) wins a free kick in the defensive half.
Foul by Gary Fraser (Montrose).
Attempt missed. John McGinn (Hibernian) left footed shot from outside the box is too high.
Fraser Murray (Hibernian) wins a free kick in the attacking half.
Foul by Liam Callaghan (Montrose).
Attempt missed. Graham Webster (Montrose) header from the left side of the box misses to the left.
Corner,  Montrose. Conceded by John McGinn.
Foul by John McGinn (Hibernian).
Kyle Willox (Montrose) wins a free kick on the left wing.
Substitution, Montrose. Kyle Willox replaces Paul Watson.
Attempt missed. Paul Watson (Montrose) left footed shot from outside the box is high and wide to the left from a direct free kick.
Foul by John McGinn (Hibernian).
Kerr Hay (Montrose) wins a free kick in the defensive half.
Foul by Darren McGregor (Hibernian).
Kerr Hay (Montrose) wins a free kick in the attacking half.
Substitution, Hibernian. Brian Graham replaces Liam Fontaine.
Foul by John McGinn (Hibernian).
Liam Callaghan (Montrose) wins a free kick in the defensive half.
Substitution, Montrose. Kieran Thomson replaces Martyn Fotheringham.
Neil Lennon is still looking to add "two or three" new faces to his Hibernian squad despite opening with a 4-0 League Cup win over Montrose.