"Last month" is sort of like previous month and "in the last month" means that something happened in the duration of the past month. There isn't much of a difference otherwise. i.e. Last month I went to California twice In the last month I have gone to California twice

in the last month = during the last month

'Last month' is for use at the start of the sentence. For example: 'Last month, I ate bread' 'In the last month' is for the end of sentences. For example: 'I ate bread in the last month.' You can also use 'In the last month' at the start, if you want, but it does not sound as fluent. I hope I helped