Can an employee be penalised for not speaking Lithuanian?

     Yes, they can be penalised.

     Administrative liability is provided for in the Code of Administrative Offences of the Republic of Lithuania:

     Article 498. Failure to comply with the resolutions of the State Commission of the Lithuanian Language and the instructions of officials of the State Language Inspectorate

1. Failure to comply with the resolutions of the State Commission on the Lithuanian Language concerning the use and correctness of the official language, and with the instructions of officials of the State Language Inspectorate regarding the use of the official language, shall result in a warning or a fine being imposed on the heads of legal persons, other responsible persons or any other persons who fail to comply with such resolutions or instructions, ranging from ninety to one hundred and seventy euros.

2. A repeat offence of the administrative offence provided for in paragraph No. 1 of this Article shall result in a fine of between two hundred and four hundred euros.

     Article 499. Failure to use the official language whilst performing official duties

1. Failure to use the official language whilst performing official duties (in accordance with the established qualification category for proficiency in the official language) in state and municipal institutions and agencies, or in other legal entities, shall result in a warning or a fine for the heads of legal entities, other responsible persons, or a fine of between sixty and one hundred and forty euros for persons who fail to use the official language.

2. A repeat offence of the administrative offence provided for in paragraph No. 1 of this article shall result in a fine of between one hundred and forty and three hundred euros.