This is marked on the 1840 1in. OS map at approx SJ 391 865. This is about 1km from both the Calderstones (which are shown on the same map), and Robin Hood's Stone (which isn't). Solomon's Tomb is not marked on larger-scale maps from the later 1840s, which do mark Robin Hood's Stone.
The map pre-dates the development of Aigburth and the area is otherwise shown as mostly fields and a few isolated houses.
The name (and the proximity to a group of ancient sites) seems suggestive of a monument of some sort, but it seems to be unrecorded and undiscussed in any of the learned papers on the Calderstones etc.
Of course, it could just be a field name, but does anyone have any info?
The site is now occupied more or less by Rockside Road.