Celtic face a side sitting second bottom of the third division as they begin the defence of their trophy at Balmoor.
In contrast the Hoops have won their 10 league games in a row to sit top of the pile in the Scottish Premier League.
However, Lennons side were dumped out of the Scottish Cup at the semi-final stage in 2010 and they were given a tough test by minnows Berwick Rangers in the fourth round last season.
And Lennon, who is keen to see his league form continue, said he wouldnt take the third division side lightly.
"You would like to keep the momentum going but its a cup competition. We're the holders of and one we would dearly love to win," Lennon said.
"We went to Berwick last year and it was a difficult night so were not going to underestimate Peterhead and momentum is important on a run like this."
Also on Sunday Old Firm rivals Rangers face a trip to Gayfield to take on Arbroath.
The Ibrox side have a selection crisis heading into the game with the side second top of the Second Division.
Midfielders Lee McCulloch and Steven Davis are both suspended for the game while manager Ally McCoist revealed the club might have to do without Kyle Lafferty and Steven Whittaker for around seven weeks through injury.
"Its not particularly good news for Kyle," the Rangers manager said.
"He looks to have a tear in the hamstring and all indications were that was going to be the case judging by the way he pulled up.
"At this moment he is on crutches and we think probably six or seven weeks Im afraid. Steven Whittaker is going down next Tuesday or Wednesday to see the specialist regarding his groin problem and it will be determined then if he needs surgery."
Croatian striker Nikica Jelavic, who missed Mondays match with Motherwell with a groin strain, and Kirk Broadfoot both face late fitness tests for the match.
Elsewhere on Saturday, Scottish Junior Cup holders Auckinleck Talbot face their biggest ever match as they take on Hearts at Tynecastle.
Fixtures (1500 GMT unless otherwise stated)
Dundee v Kilmarnock (1230), Airdrie United v Dundee United, Cowdenbeath v Hibernian, Falkirk v East Fife, Forfar v Aberdeen, Hearts v Auchinleck Talbot, Inverness CT v Dunfermline, Livingston v Ayr United, Motherwell v Queens Park, Partick Thistle v Queen of the South, Raith Rovers v Morton, Ross County v Stenhousmuir, St Johnstone v Brechin, St Mirren v Hamilton
Arbroath v Rangers (1245), Peterhead v Celtic