Question

This is the house that I lived two years ago. This is the house I lived two years ago.

这两个定语从句对吗？为什么？
某些在从句中充当时间，地点或原因状语的"介词+关系词"结构可以同关系副词when 和where 互换，例如：
This is the house in which I lived two years ago.
=This is the house where I lived two years ago.
That有时可以代替关系副词 when, where 或者why引导定语从句表示时间．地点或原因（百度百科）
那么，是否上面一句句子可以改为：
This is the house that I lived two years ago.

That有时可以代替关系副词 when, where 或者why引导定语从句表示时间．地点或原因，that也可以省去。那么，是否还可以演变成：
This is the house I lived two years ago.
如果错的话，错在哪儿了？

Answer 1

一般定语从句中，that 如果在从句中做宾语，那是可以省略的，如果在从句中做主语不可省
本句live 是不及物动词，that 又做的是从句的宾语，所以想要让不及物动词接宾语，必须搭配相应的介词in 。但是定语从句中一般如果在关系代词前面加介词，就不用that,要用which.所以最后一句错了，this is the house in which I lived two years ago.=this is the house where i lived two years ago.

Answer 2

This is the house I lived two years ago.
在lived后面加个in 就可以用了。
This is the house I lived in two years ago.

Answer 3

that不可以省略

Answer 4

This is the house that I lived in two years ago.