A:Answer It fits in an HP Pavilion Desktop 590-p0047c which is a fairly small case, if that is any help.
The 2 biggest issues will be clearance for the length and height, from the specs for the H320, the card is probably too tall to fin into the Lenovo case, you will probably need a low profile card.
It looks like there is enough room in the case for the length but it will depend upon how the interior of the case is laid out.
As long as the power supply provides more than 300w, I don't believe that there would be any power issues, the card does not require an additional power supply connector.