Thierry, what is being asked is how the LCD connects to the PIC. SPI needs an enable signal, a clock signal and a data signal. The "1602" with it's HD44780 needs 4-bit (or 8-bit) parallel data, an enable signal, a register select signal and optionaly a read/write signal as well. That's obviously too many signals to pass through a PIC with only 4 external connections. So your requirements are conflicting unless you use an external SPI to parallel converter or "expander".
I think a PIC 10F220 can do it if the interface is one analog voltage in and three SPI outputs but it's doubtful there is enough RAM to store say 10 readings then average them. It might be possible but would would take careful coding, especially as the result would involve a 16-bit product term If you change to a 12F1822 or 12F1840 type of PIC you have far more resources and can easily use 'C' as the programming language if you find assembly language difficult. They still only have 8-pins so the problem of interfacing to the LCD is still there. If you want to use the HD44780 without an additional port expander the cheapest and simples option is to move to a PIC with sufficient ports. My preference would be one of the 16F series with an on-board ADC.
Brian.