A passport or ID is all you need to start.
Standard EU procedures apply to EU citizens who want to live and work in Lithuania. To stay for up to 90 days, you only need to bring your ID card or passport with you.
If you want to stay longer, you need to acquire a certificate confirming your right to temporarily reside in Lithuania. To do that, you have to submit your application through the Lithuanian Migration Information System MIGRIS. You’ll need to provide a valid travel document and proof of your reason for staying in Lithuania, such as an employment contract. In addition, you will be required to pay a small fee of €8.60 for issuing a certificate.
You can find more information about the procedure and the necessary documents here.