Yes, you can eat lizardfish. The Food and Agriculture Organization of the United Nations (FAO) describes lizardfish flesh as being of good quality and flavour, though bony.
Lizardfishes (family Synodontidae) are bottom-dwelling fish found on open flats or around reefs, down to more than 500 metres deep, where they lie still and dart out to seize passing prey. They are easy to recognise by their lizard-like head and the rows of small, pointed teeth that show even when the mouth is closed. FAO’s identification sheets for the Western Indian Ocean report that about 9,700 tons of lizardfishes were caught in that area in 1981. Several species are taken with bottom trawls or small-scale artisanal gear and sold fresh, and the brushtooth lizardfish (Saurida undosquamis) is also sold dried and salted. That species has spread into the eastern Mediterranean through the Suez Canal and is now an important food fish in the Levant Basin. The main drawback at the table is the bones, not the taste.
Source: FAO Species Identification Sheets, Fishing Area 51: Synodontidae (lizardfishes)
Image: Atlantic lizardfish (Synodus saurus), Etrusko25, public domain, via Wikimedia Commons.