I'm going off of the first edition, but I think the second edition is very similar.
Genki is separated into two parts; the first half of the book focuses on grammar and the second half on reading and writing.
So ideally you should be doing one grammar and one r/w lesson at, sort of, the same time. So Lesson 1 in the first half of the book goes along quite well with Lesson 1 in the second half. In fact, the first two r/w lessons are about the kana, and as such, the first two lessons of grammar use more romaji.