While the Tukkers have taken two points from as many games so far, their rivals from Rome are top of the table following back-to-back wins.
Match preview
Although both of their Europa League fixtures this season have finished 1-1, given the calibre of opposition faced, Twente may not be dismayed by their failure to taste victory thus far.
The Tukkers fought back to hold Manchester United to a draw at Old Trafford on the opening matchday, and last time out they took a point from their first home game, against Fenerbahce.
However, that does mean that Twente are winless in nine Europa League matches before returning to action on Thursday.
Since letting victory slip from their grasp against Fener, Joseph Oosting's side have lost to Feyenoord and drawn with RKC in the Eredivisie, where they sit sixth in the standings.
Following Carel Eiting's last-gasp leveller at the weekend, they have now scored in 21 straight games across all competitions - a run that dates all the way back to March.
Now, Twente tackle Italian opposition in either the Europa League or its predecessor for the first time since beating Juventus in the 1975 UEFA Cup semi-finals, when they won both legs but then lost to Borussia Monchengladbach in the final.
After a convincing win over Dynamo Kyiv on the opening matchday, Lazio continued their fine start to the league phase by beating Nice 4-1 at home earlier this month.
Top scorer Taty Castellanos netted twice at Stadio Olimpico to put the Biancocelesti top of the table on six points from a possible six.
Their quest for a top-eight finish - which would bring automatic qualification for the last 16 - has therefore enjoyed the perfect beginning, and Marco Baroni's boys are intent on extending that flawless record.
Only twice before have Lazio won their first three European games of a season, but their free-scoring start suggests they could do so again this week.
The capital club have racked up more goals than any other side so far (seven), while only Elfsborg - who recently beat their arch-rivals Roma - have a higher shot conversion rate.
Ahead of last week's defeat to Juventus, Lazio had claimed maximum points from four consecutive fixtures across Serie A and the Europa League, representing their best run since the turn of the year.
However, a superb record in Rome is not matched by similar form on the road: following their 1-0 loss in Turin, they average under one point per league game away from home.
FC Twente Europa League form:
D
D
FC Twente form (all competitions):
W
D
W
D
L
D
Lazio Europa League form:
W
W
Lazio form (all competitions):
L
W
W
W
W
L
Team News
Twente's most notable absentee on Thursday night will be Moroccan midfielder Younes Taha, who is sidelined until 2025 by a leg injury.
Joseph Oosting could make a handful of changes to the side that scraped a late draw in Waalwijk last week, but Michel Vlap - scorer of the opening goal against Fenerbahce - and Sem Steijn are likely to keep their places.
Following another strike on Saturday, the latter has now been directly involved in nine of his team's 16 league goals this season.
Meanwhile, Marco Baroni will rotate his squad again, after making several changes to Lazio's usual lineup in both Europa League games so far.
Dutch forward Tijjani Noslin misses out on a return to his homeland, having been handed a three-match ban by UEFA for violent conduct, while Manuel Lazzari is struggling to overcome a thigh problem.
Taty Castellanos and Boulaye Dia have both netted twice in Europe this term, and either striker should start up front at De Grolsch Veste.
FC Twente possible starting lineup:
Unnerstall; Van Rooij, Bruns, Hilgers, Salah-Eddine; Vlap, Regeer; Van Bergen, Steijn, Rots; Lammers
Lazio possible starting lineup:
Mandas; Marusic, Romagnoli, Patric, Pellegrini; Rovella, Vecino; Tchaouna, Dele-Bashiru, Pedro; Castellanos
We say: FC Twente 2-2 Lazio
Having been handed a tough start to their fixture list, Twente may have to settle for a third successive Europa League draw.