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Under EC Directive 1991/439, a valid driving licence issued by one EU country MUST be recognised in all other EU countries. A driving licence in standardised EU format which is issued by an EU country is valid throughout the EU, and, as the holder of a LithuanXXXXX XXXXXcence holder who is resident in the UK, you are not required to exchange your driving licence for a British one, provided that it is in the standardised EU format.
In the UK, "mopeds" are defined as motorcycles with an engine size no larger than 50cc. With a driving licence obtained before 2001, you can use your licence to ride a moped (without the need to take the Compulsory Basic Training). This is confirmed here:
Since 2001, in the UK, in order to ride a moped, you will need to undertake Compulsory Basic Training (CBT) and have your licence endorsed (which will require you to exchange your LithuanXXXXX XXXXXcence for a British one):
In case you face difficulties in obtaining the exchange of your licence or the CBT testing place does not recognise your LithuanXXXXX XXXXXcence (which I know can sometimes happen), I can refer you to a free on-line legal advice service of the European Commission, which can assist you further.
I hope my answer was useful to you.
As I said, Your Europe Advice should be able to assit you in case you face difficulties in having your Lithuanian driving licence recognised: