The Hoops are looking to win their first match in five after three successive defeats in all competitions, while the visitors are hoping that there will not be a repeat of last season's 7-0 thrashing at Celtic Park.
This last week for Celtic has been nothing short of disastrous and much has rightly been made of the Hoops' recent run, which has seen them win just two of their last 10 matches in all competitions.
Nevertheless, after seeing the Hoops knocked out of two different competitions within a week as well as sitting 11 points behind rivals Rangers in the Scottish Premiership – albeit with two games in hand – Celtic's miserable run of form is something that most fans cannot tolerate.
The Hoops head into Sunday's match against St Johnstone under huge pressure from the supporters to get a positive result, but Celtic do have a strong record against the Saints in recent seasons.
Lennon's side are unbeaten in 13 league meetings with St Johnstone – winning 11 times and drawing the other two – since a 2-1 defeat away from home in May 2016.
Celtic have also won 20 of their last 22 home league matches, with the only exceptions in this run being against Rangers, most recently the 2-0 loss in October. The last time they last lost back-to-back home league fixtures was in May 2004 under the management of Martin O'Neill.
Victory on Sunday would be their 10th in the Scottish Premiership this campaign and also their 10th successive triumph against St Johnstone.
St Johnstone's impressive run of form continued last weekend as they came from behind to beat Motherwell 2-1 away from home in the Scottish League Cup, which has earned them a quarter-final tie with Championship side Dunfermline.
The Saints are now unbeaten in nine of their last 10 matches in all competitions, with their only loss being a 4-3 defeat on penalties to Dundee United in the League Cup.
Their last league defeat was in early October against this Sunday's opponents – a 2-0 loss at McDiarmid Park – but St Johnstone boss Callum Davidson is hoping that his side have learnt from their last meeting and that they can capitalise on Celtic's poor run of form.
The Saints however do not have a good record against the Hoops, having failed to score in each of their last eight league games against them, losing their last six in a row by an aggregate score of 22-0.
St Johnstone's last victory at Celtic Park was a 1-0 league win in March 2015, and if the three points can be secured again this weekend, they could move into the top six in the Scottish Premiership.
Celtic Scottish Premiership form: WWLDWD
Celtic form (all competitions): LWDLLL
St Johnstone Scottish Premiership form: LWDWDD
St Johnstone form (all competitions): WLWDDW
Celtic winger Mohamed Elyounoussi, who has scored 10 goals in all competitions this campaign, has been ruled out for a few weeks with a muscle injury.
Defender Shane Duffy, who was not in the squad that faced AC Milan, remains doubtful after suffering a knock to his knee in training.
Jeremie Frimpong is likely to start in his natural position at right-back rather than the advanced wide-right role that he played against Milan.
Captain and central defender Jason Kerr is back in contention to start on Sunday after recovering from a knock to his head, which ruled him out of the last match against Motherwell.
Celtic possible starting lineup:
Bain; Frimpong, Ajer, Jullien, Laxalt; Brown, McGregor; Christie, Rogic, Elyounoussi; Edouard
St Johnstone possible starting lineup:
Clark; Kerr, Gordon, McCart; McNamara, McCann, Craig, Tanser; Wotherspoon, O'Halloran; May
We say: Celtic 2-1 St Johnstone
Celtic are increasingly losing touch with their rivals Rangers at the top of the Scottish Premiership and given their recent form and with what is at stake, this is a must win for the hosts. However, with St Johnstone only five points off the bottom of the league, they would also welcome the three points. Neil Lennon will be desperate for a positive result and they may finally get that on Sunday.