I think the difference here is quite subtle, but we tend to 'study a lot of German', or 'we study a lot of science'. In fact, 'we study maths', or 'we study science'. The 'of' belongs to the extra phrase 'a lot of' that you are wanting to include. Therefore, 'we study... a lot of...' and 'We study a lot of' is quite correct. I hope that makes sense.