That code should run fine on your 690 with any parallel HD44780 compatible lcd.
Although the data ends up in the lcd, there are several slightly different ways of collecting and outputting the data.
The Mikro is one way, but do not spend a lot of time trying to understand what is quite a complicated routine - just use it and concentrate on getting the data ready to send out.
Be aware that the lcd need its data in the Ascii format like movlw 'H' , however if you want to send out data from a variable that is in hex you need to convert it to Ascii format first - there are several bits of code around for doing that
These 2 pdfs on this link are excellent if you want to really understand all about lcds.