He is the man who lay under the tree and read books yesterday.
He is the man who read books lying under the tree yesterday .可不可以改成He is the man reading bookslyingunder the tree yesterday不好, 你句中的reading books 是the man 的定语,表明"他现在正在看书", 而伴随状语lyingunder the tree yesterday又是表示的过去的情况,时间上有点混乱. 要么像我的答案中那样用定从,要么把is 改成过去式was .即:He was the man reading books ,lyingunder the tree yesterday./He was the manlyingandreading books under the tree yesterday