All the Lexiters I know in rl or online do indeed criticise the soft left & New Labour
BUT
all of them criticise the Tory right wing far more
A genuine Lexiters would be e.g. criticising Boris's tax giveaway to the better off,
not always going into whataboutery or diversion onto New Labour's sins
What Lexiter would keep criticising the last Labour govt & PMs from 1997-2010 (!)
when there is so much more & more recent to criticise about austerity, Tory cuts and Tory financial sleeze?
I've never known genuine Lexiters who defend Boris, Redwood, JRM and were "inspired as a feminist by Thatcher" 
The only ones I know who continually excuse the hard right and attack centre / left politicians - and express a preference for Corbyn -
are those on the hard right who - rightly - think Corbyn is their best weapon against Labour coming to power