This is the 18418th most frequent Korean word.
시간조차
"시간조차" means "even time."
시간조차 is used to emphasize the lack of even as basic as a concept of 'time' for an activity, here 'having lunch'.
그는 오늘 일이 너무 많아서 점심을 먹을 시간조차 없었다.
He had so much work today that he didn't even have time for lunch.
시간조차 here emphasizes the complete absence of time such that it affects social interactions in the form of meeting friends.
그녀는 바빠서 친구를 만날 시간조차 네 달 동안 없었다.
She was so busy that she didn't even have time to meet friends for four months.
In this usage, 시간조차 is employed to humorously stress the irony of having excessive free time leading to no time even for feeling bored.