I'd like to buy a cake with a lots of strawberries.

lot后面不加s

要么是a lot of
要么是lots of。

是的，是复数。
lots of 和a lot of 都是很多的意思。

只能是lots of或者a lot of，没有a lots of，要熟记

I'd like to buy a cake with a lot of strawberries.

许多：many ,a lot of ,lots of

是的，两个选那个写都一样。
that 一定要，因为that做宾语从句中的主语。

这是一个宾语从句不能省略that. I'd like to buy a cake that with a lot of strawberries.