It is a totally new phenomena in Lithuania, if compare with the soviet times. If You want to find the roots of that during soviet times in Lithuania, care of soviet youth organizations for example, for elderly, or for war veterans, partially resembled the phenomena of volunteering, but it had another, different meaning than volunteering in the present times. The interwar independent Lithuanian history (between 1918-1940), however, gives examples of volunteering mostly in health and social services in Lithuania.
Financially, volunteering in the United States is worth over $167 billion USD (Corporation for National and Community Service, 2018). Many nonprofit organizations in the U.S. cannot afford a traditional full-time staff, so the services provided by volunteers keeps our nonprofit sector functioning. I don't think a lot of us care about the financial value we contribute to the nonprofit sector, however; which is odd when one considers that almost everything in the U.S. is a business or is close to having a privatized version of itself. The national culture, as of now, is also very selfish, so I am surprised that so much volunteering is still being done.
Reference
Corporation for National and Community Service. (2018, November 13). Volunteering in U.S. hits record high; worth $167 billion. https://www.nationalservice.gov/newsroom/press-releases/2018/volunteering-us-hits-record-high-worth-167-billion