because you are an EU-citizen, you have the possibility to transfer gained rights according to the Unemployment benefits Scheme in Lithuania to Denmark.
You can read more about requirements for this in our article about this topic: https://a-kasser.dk/transfering-periods-of-work-and-insurance-from-another-eea-country/
And you dont need to apply for work-permit. As an EU-citizen you are allowed to work and stay in Denmark. So in this way you meet some of the requirements for being able to get unemployment benefits.
But to be able to apply for unemployment benefits in Denmark one of the other requirements is that you must have been member of an A-kasse (Unemployment Insurance Fund) in Denmark or Lithuania for at least 1 year.
You dont tell us if you currently are member of an Unemployment Insurance Fund (or similar) in your home country Lithuania.
If you are not - then you will have no chance to get Unemployment benefits if you move to Denmark now.
And the 1 year membership period is only one of the requirements - another is that you must have earned at least DKK 223,428 (in 2017) during the last 3 years (in total). Only income earned during membership periods are counted. Also here both income earned in denmark and Lithuania can be used to fulfill the income requirement.
According to the information you have provided, it seems for us that you can not meet these two main requirements for being eligible for Unemployment benefits.
We are only able to guide you about rights to Unemployment benefits ("dagpenge"). If you need to know if there is any other support you can get, you could try to contact The Danish Agency for Labour Market and Recruitment, or try to find answers on their website www.star.dk
Best regards, and happy new year!