Killie are surely travelling in hope rather than expectation as the Ayrshire side have lost 30 of their last 37 away games at Celtic in all competitions.
It has been an interesting time at Celtic Park in recent weeks, with manager Lennon coming under real pressure in the wake of his team's exit from the League Cup at the hands of Ross County at the end of November.
That shock defeat saw fans protest violently outside Celtic Park, and led to calls for Lennon's dismissal from some quarters, though the club's board insisted they were standing by the Ulsterman.
Lennon is still under some pressure as results have not been impressive since that League Cup exit, with the Hoops losing to AC Milan in the Europa League and drawing 1-1 at home to St Johnstone last weekend in the Premiership.
A 3-2 midweek Europa League home win over Lille at least provided some solace, though it could not prevent the Celts finishing bottom of Group H.
David Turnbull made his European debut in that game, netting the winner, and has surely put himself in contention for Sunday's match.
The Bhoys are still a domestic powerhouse, though, as shown by the fact that they are undefeated in 36 of their last 38 home league matches.
Kilmarnock have endured some COVID-19 related controversy this week along with fellow Premiership outfit St Mirren, with the two clubs being punished for breaching health regulations.
Killie's scheduled game with Motherwell on October 2 was called off due to a coronavirus outbreak at Rugby Park, resulting in a referral to an SPFL tribunal.
That tribunal handed down a walkover 3-0 defeat to Killie for the game, and also issued the club with a £40,000 fine, suspended until June 2021.
The club are receiving legal advice as they mull over whether to contest the outcome of the tribunal, which they found "disappointing."
Killie have enjoyed mixed form in the league in recent weeks, winning two and losing four of their last six outings in the Premiership, and also failing to reach the knock-out stages of the League Cup.
Last week, the men from Rugby Park slipped to a 1-0 defeat away at Hamilton Academical, with Clevid Dikamona receiving a red card after just 29 minutes.
Celtic Scottish Premiership form: WLDWDD
Celtic form (all competitions): DLLLDW
Kilmarnock Scottish Premiership form: WLLLWL
Kilmarnock form (all competitions): LLWWWL
Neil Lennon made six changes to his team in midweek and it appeared to work, with the Celts beating Lille 3-2. Shane Duffy and Conor Hazard both started in that game and could well retain their places on Sunday.
Celtic possible starting lineup:
Hazard; Frimpong, Ajer, Jullien, Laxalt; McGregor, Soro; Christie, Turnbull, Elyounoussi; Edouard
Kilmarnock possible starting lineup:
Rogers; McGowan, Broadfoot, Rossi, Haunstrup; Kiltie, Power, Tshibola, Pinnock; Kabamba, Brophy
We say: Celtic 1-1 Kilmarnock
We are backing Killie to come away from Parkhead with a well-earned point this weekend, after holding the Celts to a 1-1 draw.
Celtic may have managed to win in midweek, but their domestic form has been really poor in recent weeks as pressure on Lennon mounts.
We expect the men from Rugby Park to add to that pressure after frustrating the Celts with a resilient display that is sure to lead to more discontent from the Celtic fans.