After more than one year of experience now...
Deutsche Post is the only (casual) service which delivers to Lithuania, and all their parcels will be delivered by their partner itella. Itella now have parcel stations, but one can not give the address of a station as delivery-address. They try to bring the parcel to the home, and if there is nobody they will place it into such a station. Then they will send a message and a code to a phone number they associate with the home-address.
Sounds good, but in real life this means: if you have an address unusual or hard to find, you will never get your parcels to your home. Second, it is needed you write your phone number onto every parcel. This is hard, if you get a parcel from your beloved grandma, who forget to add the phone number, or if there is no option to add one if you order things.
Next problem is that it seems to cause problems, if a non-Lithuanian phone number would be used. Sometimes you get the message "Parcel arrived" only and need to call to get the code to open the station. Other times you get a code and do not know at which station the parcel waits. More than 25% of times I got nothing. IF I knew, there will be a parcel, I called itella and asked for it (problem, if you have no parcel ID...) and recently (last month) we got two messages, that our parcels came back from Lithuania to the sender...
My solution now: I (ab)use an address in Germany to collect orders or parcels for Christmas/birthdays and so on. Then my family put all in a big cardboard box and I book DHL or DPD to get it from this address and bring it to my address in Lithuania. They need 1 to 2 days to deliver.
Sadly this do not solve all problems, so I would be happy for any advice others could give :)