I think the people who are saying that LS must have resigned are doing so out of sentiment. It seems perfectly clear from his comments after the Gateshead match that his thoughts weren't tending that way at all. As I read it, he was sacked but the club rightly wanted to put it in kinder terms than that.
I too would like to thank LS for all he's done at the club and wish him well for the future. I wonder, when he reflects on his time at Alty, whether he might think that he could have thrown himself into the life of the club a bit more? The relationship between a manager and the fans is in part an emotional one but LS always seemed too distant and impassive for us to really take him to heart. The fact that we barely ever sung songs about him always struck me as significant. Of course a manager has to be himself and do the job in his own way but I do think he could have shown more of himself - when he was appointed, GR picked out his enthusiasm as a key point but that wasn't a quality that ever came across particularly. I'm sure it was there but we never saw it. I think if he could pepper his calmness and dignity with a bit of blood and thunder now and again, he'd be a better and more inspiring manager for it.