Depends what you mean by warmer weather or lighter leather. Both things are context dependant. Capeskin his probably the lightest followed by some goat (some is heavy) and 2.2 oz steer or horse. No leather jacket is much good in warmer weather. But warm here means 115 degrees. All makers will produce something lighter if you ask them.
At the risk of incurring the wrath of the faithful... lambskin is lighter than goat or cow.
Yes, it's also less tough than other hides, and thus a poor choice for a spec military jacket or motorcycle jacket. But it's still leather, and nowhere near the tissue-paper fragility folks here often dismiss it as having. Lambskin is fine for ordinary wear, plus it drapes beautifully. I've been wearing a lambskin Wested Raiders jacket with an all-cotton lining as my "summer weight" leather for 15 years. It's comfortable over a short-sleeve shirt up to the low 70s, as long as it's not blazing sun and/or high humidity.
As Seb said, no leather jacket will be comfortable in really warm weather. But a thinner leather like lambskin and a cotton lining (and having no wrist or waist knits) is more tolerable, IMHO. Don't dismiss lambskin out of hand unless you need a sturdier leather for hard use.
I like Thedi's selections in my warm (los angeles) climate. His horsehide that I have is soft and pliable. Diamond Dave's steer is very nice too, I tried on a Buco J-100 recently, and it was a perfect weight IMHO. Shinki is fine for the evenings when it cools down a bit, but my FQHH CXL is definitely saved for colder climates.
I've had vintage goat, but it has different qualities that I dont really like.
Lambskin is very light but most of the top quality makers (as you put it) will not use it. I personally have had two or three lambskin jackets each of which tore open for no particularly reason. I did mention capeskin which is sheep hide - adult lamb if you like - that has the weight of lamb but more strength. A number of the premium makers use capeskin. As Doctor Strange alludes the Indiana Jones jacket in the films was made of lamb. Some people seem to be able to wear Wested lambskin jackets for years without issue. Wested are not a premium maker (I've owned two of their jackets) but they make reasonable jackets some people really like.