There is but a single Lithuanian restaurant left within the city limits.
Seklyčia is the last Lithuanian business in the Marquette Park neighborhood which used to be very heavily Lithuanian.
Two other Lithuanian restaurants are literally across the street from Chicago and are not difficult to get to using public transportation.
You know about
Grand Duke's, in Summit, near the busy corner of 63rd & Harlem. From downtown, take the Orange Line elevated train to Midway Airport, about 30 min. Transfer to the 63W bus (westbound; toward 63rd/Archer) and get off at Harlem (7200W; about 15 min). Don't forget to visit their delicatessen, in a separate building next door. If I had to choose one restaurant, this would be it.
Mabenka is also in the vicinity of Midway, but south (Duke's is west). Orange Line to Midway, then transfer to the 54B bus (southbound; toward Ford City). Get off at 74th Place (last stop on Cicero; about 10 min) and walk 5 blocks south. There are other buses (PACE) that go to 79th but they would require a separate fare.
The other Lithuanian restaurants are in more distant suburbs not easily accessible by public transportation.
You might also be interested in the
Balzekas Museum of Lithuanian Culture, on Chicago's southwest side.
Seklyčia
2711 W 71st St
Chicago
773-476-1680
Grand Duke's (Kunigaikščių Užeiga)
6312 S Harlem Av
Summit IL
708-594-5622
Mabenka
7844 S Cicero Av
Burbank IL
708-423-7679
Balzekas Museum of Lithuanian Culture
6500 S Pulaski Rd
Chicago
773-582-6500