Where to apply manual delay in character LCD
You should be looking at the datasheet for the LCD module, not at a typical application.

Anywhere the datasheet says you must meet a minimum delay time you need to make sure that you meet that delay. For the example timing diagram you provide, it looks like enable must be high for at least 450ns and its period must be at least 1000ns. You also need to make sure you meet the setup and hold times for R/S, RW, and DATA.
Depending on how fast your processor can toggle a GPIO line you may need several short delays in the software.