帮看看这两个英文句子是否有语法错误？或者怎么改更通顺些

第一句有点不太舒服，而且and后面的半句话，缺少系动词。
There is a lack of evience to understand the theory which has some contradictions with facts.

cautious改为precise更好一点吧。cautious在这里用的不太合适。 而且整个句子下来，如果按照你下面的汉语意思来翻译的话，你的句子存在一些出处。

Firstly, we need to do more precise and deeper research to verify these hypothesis if we're planing to do new work on the base of this theory.

仅供参考！！

1. The theory can not be justified because it's contradictory to facts and it's not well-supported by evidence.
2. We （主语自己改~）should cautiously do more in-depth researches that are based on the theory to verify the hypothesis.
（cautious是形容人的，不能形容research）

有语法错误，也很不通顺啊。。。

说实话，不知你想表达什么中文意思？？

语法没错误，但There is a lack of evidence to understand the theory意思有点不通。原中文是想表达什么？