I want to give him the benefit of the doubt and (from the outside) it is impossible to know who had the final say on transfer dealings this past summer. However, not signing a replacement for Lukaku is indefensible. He is culpable anyway you try to spin things.. and heads need to roll after that fiasco.
The people at the top will survive - Moshiri, Kenwright, etc. - such is the nature of the beast. But Walsh was intimately involved in summer player recruitment; he needs to be held accountable.
Unfortunately, with Allardyce being the apparent managerial appointment, his reckoning will not be any time soon.