Kunimoto was born in Japan to a mixed Japanese and Korean family. His father, Yoshihiro Lee, won the All Japan Karting Championship in 1983, while his uncle, Yoshihiko Lee, won the same championship in 1980 and 1981. Racing ran deep in the family — his younger brother Yuji also pursued a career as a race car driver. Kunimoto carried dual racing identities throughout his career, also known by his Korean name Lee Kyung-woo.
Kunimoto began karting in 2001 at age twelve. His talent quickly surfaced, and in 2004 he won the All Japan Karting Championship FA Class. That success earned him a scholarship from Toyota, who enrolled him in the Formula Toyota Racing School. He made his car racing debut in the 2005 Formula Toyota season.
In 2006 and 2007, Kunimoto competed simultaneously in both Formula Toyota and Formula Challenge Japan. By the end of 2007 he had won the Formula Challenge Japan championship with three victories, while finishing as runner-up in Formula Toyota.
Joined TOM'S for the 2008 All-Japan Formula Three Championship, Kunimoto finished runner-up in his first season in the category. His breakthrough came at the end of the year when he travelled to Macau with TOM'S and won the Macau Grand Prix — one of the most prestigious non-championship Formula Three races on the calendar. The victory made him the second Japanese driver to win the race, following Takuma Sato.
Throughout 2008, alongside his Formula Three campaign, Kunimoto drove for apr in the Super GT series, operating as part of Toyota's Young Drivers Program. The following year, he moved into the 2009 Formula Nippon season with Team LeMans. The step up proved difficult: he finished last in the championship standings, collecting a single point across the season.
Kunimoto joined A1 Team Korea for the 2008–09 A1 Grand Prix season, which brought together national teams in a format designed to showcase talent from across the world. He was entered for the South African round but was prevented from racing that weekend due to political issues relating to a slogan displayed on his car.
Kunimoto made his first appearance in the Formula Renault 3.5 Series at the end of the 2009 season, joining Epsilon Euskadi for the final two rounds. He replaced Dani Clos in the team's lineup at the Nürburgring and at the season finale at the new Ciudad del Motor de Aragón circuit.
He stayed with Epsilon Euskadi for a full campaign in 2010, this time partnering Albert Costa, the reigning 2009 Eurocup Formula Renault 2.0 champion. The season gave Kunimoto consistent European exposure and represented the furthest reach of his international single-seater career.
Keisuke Kunimoto's 2008 Macau Grand Prix victory stands as the centrepiece of his career — a result that placed him among a select group of Japanese drivers to have conquered that circuit. His progression through Toyota's junior pathway demonstrated both the strength of that programme and the ambition of Japanese drivers to compete beyond domestic championships during the mid-2000s and early 2010s.