Loss of peripheral vision from droopy lids?

Sometimes. If the upper eyelid skin becomes very redundant and hangs over the lashes that can reduce the peripheral vision. This can be detected in a visual field test. This is one of the common reasons that eyelid surgery -blepharoplasty- is performed.
Can be fixed. Droopy lids fall over the eye and start to obstruct the superior peripheral field. In more advanced cases they can actually obstruct the center and require painful tilting back of the head and neck to see. This is documented on a visual field and this information used to support insurance coverage of blepharoplasty which can fix this condition.
Absolutely. Loss of peripheral vision can occur from brain problems or retina problems, as well, but skin can be a frequent culprit. This can occur in several ways. The lid, itself, can droop due to weakened opening muscles (ptosis). The skin over the lid can hang down below the eyelashes due to excess lid skin or due to descent of the eyebrows over time, simulating excess lid skin. All can be fixed!