Hi Jed.
I was there early to mid September in 2014. Lima Tshirt/sweater by day, though it is prone to drizzle. We had good weather at Lake Titica/Puno Tshirt/sweater by day. Cusco good weather too, Tshirt - though one late afternoon it did rain so be prepared for this too. Machu Picchu same again - T-shirt though be prepared for anything - you'll leave hotel very early and be out til late.
As you say conditions vary so take layers including a jacket. When we were there when the sun went down it got real cold - don't go on a trip in the afternoon like me in Cusco and be caught out later without a sweater/jacket when the sun is setting - chilly. From Titicaca to Cusco we had snow blowing in the wind at a high pass then hot conditions in the valley, all in one day.
Others might tell you different but this is what I experienced. I hope of some help??!
I so loved this trip. Do enjoy.
Angie
