It is not "obviously" unlawful. Far from it. The Divisional Court ruled in favour of the government. It is still possible that the Supreme Court will decide that the Court of Appeal has overstepped the mark.
The Public Law Project's statement on the case somewhat overplays the extent of the judgement. The Court of Appeal has decided that some details of Regulation 33 of the Civil Legal Aid (Procedure) Regulations 2012 frustrate the purpose of the Legal Aid, Sentencing and Punishment of Offenders Act Schedule 1 paragraph 12(9). The effect of this is that the time limit of 24 months in the regulations needs to be lengthened and the regulations need modifying to include provision for victims of financial abuse. It is impossible to be certain but there is certainly a good chance that the Supreme Court would overrule at least part of the Court of Appeal's judgement if the government chooses to appeal.
I accept that this is now Gove's responsibility but he did not make the current Regulations and has had limited opportunity to amend them given that any amendment has to go through Parliament. If he had been arguing passionately in favour of the current Regulations I would agree that it is egg on his face. In the context however I really don't see it.