Ichihara, Imahira and Lee all shot overall scores of 10-under par and tied for second place in The Open Qualifying Series event, finishing one 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 his fourth Open Championship based on his world ranking of 114th.