Ichihara, Imahira and Lee all shot overall scores of 10-under par and tied for second place in The Open Qualifying Series event, finishing 1 shot behind winner KT Kim.
Ichihara will make his second career Open appearance after playing in 2012 at Royal Lytham & At Annes. The native of Japan fired a 68 in Sunday's final round at JFE Setonaikai Golf Club.
"It's very exciting to play in The Open again this year," Ichihara said. "My first time was four years ago -- it was my first major and I didn't know what to expect. I found it hard to play my best as I was very intimidated.
"This time I will know what the experience is like and I hope to be able to focus on playing my own game."
Imahira, 23, will make his first appearance in a major at Royal Troon.
"I am really excited to be going to Scotland to play in such a special event," he said. "In my mind I think of the links courses as being very hard and fast. ... Since it will be my first real links course and first major, it's going to be a very tough challenge but I am very much looking forward to it."
Tanihara, 37, will play in The Open for the fourth time based on his world ranking of 114th.