Peter,
Basic text is the easiest to drive one of these character LCD displays but I imagine it could be done relatively easily using blocky or flowhart as well but all the programs I know of are in basic. I've never seen one of these programs in blocky or flowchart but I've never looked for one.
Some background info.
The character LCDs have a parallel bus with 8 pins D0 - D7 and 3 control pins. For just writing characters to the LCD we wire one control pin to 0V and use the other 2 control pins and the LCD also has a mode where you can use just the 4 data pins D4-D7 so that means the chip you use to drive the LCD must have at least 6 outputs.
The point I want to make here is that to write to the LCD you need 6 outputs so you will not be able to drive a character LCD directly using an 18M chip.
It is common for people to want to run their program on a PICAXE chip and use a serial pin to write characters to the LCD, for example using SEROUT, so the layout becomes like this:
The PICAXE chip on the left is sending SEROUT commands to a FRM010 chip in the middle that reads the serial characters from the PICAXE and writes the characters to the LCD using the 4 data pins D4-D7 plus the two control pins RS and E.
The FRM010 chip was sold by Rev-Ed but it can by any chip programmed to read serial characters in and write them out to the LCD.
The Rev-Ed AXE133 LCD you mentioned does exactly this. It has the LCD display plus a pre programmed 18M2 PICAXE chip.
Rev-Ed also make the axe133.bas program available to download here
axe133 together with the AXE133 datasheet which has a circuit diagram showing you how to connect the programmed 18M2 to the LCD so you can build your own AXE133 if you choose to.
The advantage of this setup is that the PICAXE chip on the left in the diagram only needs to use one output pin to send serial characters and the program only needs to have SEROUT commands which take relatively little program space.
The disadvantage is that you have to pay for another PICAXE chip to do the serial to parallel LCD conversion.
Another opton is to use an I2C "Backpack" in the middle. This is most often a cheap PCF8574T serial to parallel chip. It is not a real I2C chip but you can write a basic program for the PICAXE that drives it using the PICAXE I2C coammands.
This has the advantages that it is cheaper than using a PICAXE chip to do the serial to parallel LCD conversion and it only uses 2 pins on the left hand PICAXE but it has the disadvantage that the program in the left hand side PICAXE is more complicated and so larger.
If you see "16X2 LCD Display for IIC/I2C/TWI/SPI Serial Interface Module For Arduino" on ebay then it is an LCD that has one of these PCF8574T based I2C Backpacks on the back:
I have not used one of these PCF8574T based I2C Backpacks so I can't tell you how complicated they are to use or how much code it adds to the program in the left hand PICAXE.
Do you have any other PICAXE chips?
There is a very straightforward basic program written by the forum member marks for the 20X2
@marks PICAXE 20X2 driver code that could be easily converted for the 14M2, 18M2 or 20M2 chips.