Respected Apple analyst Ming-Chi Kuo says that he expects Apple to switch to an all-OLED iPhone lineup in 2020 - with a high-end 6.7" and 5.4" models and a lower-end 6.1" one. The higher-end modules will also support 5G connectivity.
This confirms WSJ's report from January 2019. It is estimated by most analysts taht Apple's 2019 iPhone lineup will sport similar displays to its 2018 one (i.e. OLED on high-end modules and an LCD on the lower-end one).
Apple's current 2018 OLED iPhones are the iPhone XS with its 5.8-inch 1125x2436 flexible notch-type AMOLED display (produced by Samsung Display), 4GB of RAM and 64/256/512 GB of storage. The XS Max has similar specifications - but with a larger 6.5" 1242x2688 AMOLED.