Egyptians noted in papyrus scripts that they used rice bran extracts and some other ingredients in potions to heal sunburn. Oddly enough, light skin was seen as more attractive than dark skin in their culture.
Fun fact: Gamma oryzanol, found in rice bran extract, is still used to this day to absorb UV and prevent sunburn.
I can't find much on the western cultures, so I'd like to hear someone else on this. It appears that many people relied on umbrellas and long clothes to prevent sunburn.
Modern sunscreen is debatable as there were many people working on a formula around the same time. In 1938, a Swiss chemistry student named Franz Greiter suffers sunburn while climbing Mount Piz Buin on the Swiss-Austrian border and set out to invent an effective sunscreen. In the 1940s, Benjamin Green was experimenting with various ingredients with a focus on "red vet pet." Mixing red vet pet, cocoa butter and coconut oil together led to a product that would eventually become Coppertone suntan cream. And in 1946, Mr. Greiter’s product, called Gletscher Crème (Glacier Cream), comes to market under the brand Piz Buin, which is still sold today. There was also in the early 1930's, South Australian chemist, HA Milton Blake, experimented to produce a sunburn cream. The founder of L'Oreal, chemist Eugene Schueller, is believed to have invented the first sunscreen in 1936.
References:
Shaath, Nadim A., ed. 2005. Sunscreens: Regulations and Commercial Development. Third Edition. Boca Raton, FL: Taylor & Francis Group.
An Old French fabliau (a rhymed, bawdy tale) from the 13th century describes an old woman “sunning herself beside a thicket” (que s’asorelle a un buisson). “[S]he sat and smeared herself with lotions / of old lard, quicksilver, and plants / over her face and on her hands / because the sun shone bright and hot” (i ongement ot fait de dokes [= dock, a medicinal plant], / de vif argent & de vis oint / don’t son visage & et ses mains oint / pour le solel qu’il ne l’escaude). Sounds like sunscreen to me--or is it sun-tanning lotion? This is from Nathaniel E. Dubins’s hilarious translation of 69 of these fabliaux published last year (The Fabliaux, pp. 347, 349).