Hi,
Yes, the address
will need to be multiplied by 2 (to $46 or 0x46) ; a "clue" is that $23 is an Odd number and PICaxe requires an Even number, because the Least Significant Bit is the Read/Write Bit which aways should be declared as a zero. It appears that the majority of web links to a "BH1750 Data Sheet" are actually to a Rohm "Technical Note" which deals with the I2C Data format in considerable detail (from about page 10 onwards).
Note that the basic BH1750 chip is rated for
3.3 volts, however many (but not all) breakout boards include an additional voltage regulator and I2C voltage-shifting transistors (usually described as "3 - 5 volts" in the listing). Not a problem as PICaxe easily runs from 2 (preferably) or 3 Alkaline cells (i.e. 3 - 4.5 volts), but be careful with a 5 volt (e.g. USB) power supply.
Personally, I've not read the data sheet in great detail, but it appears that the BH1750 needs to be instructed to make a measurement and then takes some time to calculate a result, so you may need to sprinkle PAUSES in your program.
Ask again if you need more help.
Cheers, Alan.