Kaunas train station:
Self service storage terminals. This service is available 24/7; however, you can only place your luggage for storage or collect it from lockers within working hours of the Railway Station.
Railway station opening hours: I–VII, 04:10–21:45
Website: Luggage storage at train stations | LTG Link
Kaunas Bus Station:
The storage service is provided by the delivery/shipment company – "Siuntos autobusais".