I think the problem is, if Lambert left, would a new manager want to come, when he would know that the new owners might not like him and he could be sacked within a few months of being here, if a takeover happens? To me, you're not going to get many committed managers in those circumstances, just a journeyman looking for a last payout, playing the 'committed manager to this big club' act.
If a new manager were to come, I think that you will find the same situation as we saw with O'Neill, where it is the new owner that rubber stamps the appointment.