Both of them have the same meaning, but only sentence #1 is grammatically correct.

I think that brought about is redundant, and lengthening must be lenthy . This is partly because of the lengthy summer season and climate change.

Yes, they are more or less the same. I would change them a little bit, however: 1- this is partly because of the lengthening summer season, brought about by climate change. 2- this is partly because of the summer season, which is lengthening as a result of climate change. I've used the coma to show that I'm giving some extra information about the summer season.

The first is not well written, the second is badly written. Climate change has brought about a lengthening of the summer season, i.e. in your sentences 'lengthening' should be the subject of 'brought about'. The correct version would therefore be: "this is partly because of the lengthening of the summer season brought about by climate change." Your version 2 is nonsense: the summer season existed long before climate change began, therefore it cannot have been brought about by it. Your version 1 is half way between nonsense and correct, but if read quickly enough it makes sense.