If anyone is interested, here is the optimal solution I found after my misguided foray into inverters and mains power. There appear to be readily available bulbs that run off a low voltage 12 - 24 V supply, and which have an E26 base to fit into a standard lamp fitting. These bulbs will therefore happily work with the 18 - 21 V supplied by a lithium tool battery, with no inverters or voltage converters required. This also leads to good efficiency and correspondingly economical use of the battery. The light quality is far more pleasant than the light you get from camping lanterns or work lights. In reality of course, you can put the battery on the floor out of sight, and the lamp appears just as if it were plugged into a wall outlet.
(It is important, of course, to remember that a low voltage bulb is installed. Some kind of tag on the plug would be indicated as a warning, or even a zip tie to prevent the plug being removed from the connector.)