Hampi Express that connects Bangalore and Hubli is a popular option to reach Gadag from Bangalore. The train gets you to Gadag the nearest railway station from Lakkundi in about 11 hours. Both the up and down journeys the train covers in the night, and that is one of the reasons for its popularity.
There are no luxury buses connecting Bangalore to Lakkundi, only one Rajahamsa and a Sarige is available . If possible avoid roadways as train is a far more convenient.
Lakkundi is about 400 kms from Bangalore and the nearest railway station is Gadag Jn which is just 12 kms from Lakkundi. If you are visiting only Lakkundi and there about then using train as the mode of transport is the best option.