Questions text.....

How long does it take after the filing of a trademark application for it to be granted?

At average 18 months, but not longer then 24 months.

annuity fees

Annual fees for the validity of a patent you can find on Appendix 1 on Law on Fees of the Registration on Industrial Property Objects (Article "Legal Acts" on this SPB website).

Is the use of "R" or "Registered Tademark" obligatory for a registered trademark in Lithuania?

It is not obligatory.

fees

Law on fees of the registration of industrial property objects you can find on Article ,,Leegal Acts" on SPB website.

Does the office proceed of a research on the previous trademarks during the examination of a trademark's application?

No, doesn't. The registration system of the trademarks is using in Lithuania.

Can't find "For filing an application to register a trademark - LTL 240" form on this site, and your search box does not work. If I cannot find the form and I don't know the cost, it is not likely I will be doing business! :)

"For filing an application to register a trademark (hereinafter referred to as an application) - LTL 240" means the amount in Litas (Lithuanian national currency) of the fees. A request for the registration of a mark and issuance of the trade mark certificate (ZP-1/2004 form) is in Lithuanian page ,,Prašymų formos". Please be informed that under Article 11.2 of the Law on Trade Marks of the Republic of Lithuania all actions with marks between foreign nationals who are not permanent residents of the Republic of Lithuania or in the another Member States of the European Union and legal persons of foreign states who do not have a subsidiary or representation registered in the Republic of Lithuania or a residence, subsidiary or representation in the another Member States of the European Union shall file applications to the State Patent Bureau, including also representation at the Appeals Division, through the patent attorney of the Republic of Lithuania.