I only have one tap . can i still use the speed queen lws21nw top loader

Hi from retired Englishman in SW France,
In a word- YES!
You will need to purchase, from a hardware (?) store, a 'Y' adapter. Upside down the single end (internal thread) screws into the cold water supply and the hot and cold washer pipes screw into the double end (external threads). The washer is fooled into thinking it has hot and cold! When it expects hot, it opens its hot valve but instead gets the cold water and has to heat it up. It will therefore take longer for the machine to do the washing. When it wants cold for rinses, it opens its cold valve and gets the same water! Simple ;-0)
If this has assisted you please consider a 4 thumbs up for the rating.
Thanks and good luck,
John C