Last years does not talk about a period of time immediately before the present time. It talks about a period of time at the end of something.
The word you are looking for is recently. It is when something happened not a long time ago. It talks about a period of time. It is a synonym of lately.
Last years I have been studying the work of Manet.- In the last years of his life he was very ill.
- Recently I have been studying the work of Manet.
