You Do Need power plug adapter while traveling from Lithuania to Faroe Islands.

Here is Why You Need An Adapter

The outlet and plug type used in Faroe Islands are C, E, F and K and in Lithuania are C and F. This is how they look like.

Lithuania

In Lithuania, outlets of type C and F are in use.

Type C

Type F

Faroe Islands

In Faroe Islands, outlets of type C, E, F and K are in use.

Type C

Type E

Type F

Type K