Out of interest in Wales it has happened that two groupings - Forward Wales & People's Voice - have stood their candidates as independents. In the latter case this is because of the nature of the group, outside of its core in Blaenau Gwent it has drawn in a smattering of independents from elsewhere in the valleys.
Lavalette is not an SWP councillor therefore it would be wrong to label himself as such, he is part of an organisation and periphery that include people like Valerie Wise, one time Labour-Left veteran.
Lavalette has changed his designation a few times - Socialist Alliance against War, Socialist Alliance, Respect, he could change his name to Left Alternative, but given as he probably hopes that this will be a stop-gap until some new alliance emerges, and he is probably angling to build something locally among among forces and people in the North West, the designation of independent socialist seems appropriate. In the contxt of bourgeois politics in the area he is an independent socialist.
This also reflects the modest methodology of building the Left Alternative & the nature of the organisation. The Left Alternative is not the alternative but rather a campaign/groupuscule towards building a new fighting coalition of the working class. As such, it makes sense for Lavalette rather than presenting local people interested in a broad left party with the finished article that he projects himself as holding the shape of such an alternative open - hence the designation of independent socialist is more appropriate than "Left Alternative" which would imply that the nature/shape/terrain of what he was building was already defined rather than arising out of work at the grassroots and what local activists want.