Lunar new year is known as Chinese new year, and it is normally celebrated around late January to sometime in February. This year it is on the 16th of February ( depends on the country ).
In most of the Asian countries, people celebrate lunar new year. All most all the Asian countries celebrate it, but you won't find much for the lunar new year in Japan. The reason why the Japanese don't celebrate it is told that in 1872, there was intercalary months the new year became 13 months and the government found it hard today wage for 13 months to people, so Japan stopped using lunar calendar and switched to using solar calendar but it still is not sure if that was the reason Japan changed to use solar calendar.
Chinese town in Japan of course celebrate Lunar new year, and you can see the annual lantern festival in Nagasaki. It used to be a festival only for Chinese people living there to celebrate lunar new year, but now it became an event for the whole Nagasaki city for people to enjoy the Chinese culture.
( Nagasaki lantern festival )
There are some areas in Japan that still celebrate lunar new year. Some towns in Okinawa and some other southern islands in Japan celebrate lunar new year but it is not a national holiday so the shops are open and people need to go to work. It is not celebrated like other Asian countries but people in Okinawa still put some flags out, and eat some okinawan soba like how people in main land of Japan eat soba for new years. Also they cook many pork dishes for new year. Try this recipe if you are interested in Okinawan dish!