The local election results were a good result for Labour in that if the results were simply transpositioned to a General Election then Jeremy Corbyn would be Prime Minister. Arguments saying that Labour will necessarily do worse at a real General Election don't wash.
Ok it wasn't exactly a landslide Labour surge, but Labour did improve significantly on its 2014 result. The projections made would put Corbyn into office. See https://twitter.com/JohnRentoul/status/992487750661279745
Moreover the Liberal Democrat and Green Party vote went up as well, which, indirectly is also good news for Labour for the simple reason that a lot of these voters would vote tactically for the Labour candidate in a General Election in marginal Tory-Labour seats. Hence Labour could actually end up with a significant lead in seats over the Tories at a General Election - and remember, the Tories only need to lose 10 of their current seats and Corbyn will be Prime Minister. In theory under some scenarios the Lib Dems might go with the Tories again to keep them in power, but in reality the revulsion of Lib Dems (led by Vince Cable especially) against re-visiting this option would be likely to allow Labour to form a Government.
On the other hand comparisons with Miliband's experience of doing moderately well in 2014 and then losing in 2015 don't carry much weight. Why? Well because in 2015 substantial numbers of UKIP supporters voted tactically for the Tories in order to get the EU Referendum, which turned out (for them) to be a winning strategy. But now with UKIP collapsing UKIP voters have returned to their former folds and so by definition there won't be much UKIP tactical voting at the next election, and much less motivation to do so anyway. So, in contrast to 2014, the Labour vote is more solidly placed for the next General Election. Indeed, as I have argued, the tactical voting possibilities are actually positive for Labour at the next GE, as opposed to being rather negative for them in 2015.
Hence this is a good result for Labour. The Tories face an uncertain economic future. The UK has practically the lowest growth rate among OECD countries. The 'Leavers' in the Conservative Party may say this is not caused by us leaving the EU. - But that only puts blame on the Tory Government. So, unless there's a a major upswing in the economy thing may actually be pretty good for Labour overall.