One thing that is rather important to add: there's always a tendency to project forwards from local elections, to try to read them as predictive. This was an error in the past and is an even bigger one now. The Conservatives performed poorly. Does this mean they will lose re-election at the next GE, whenever it shall be? No. Labour performed poorly in a different sense. Does this mean they will fail, once more, to break through and win a GE? No. The LibDems had their first good local election night since their post-2010 electoral collapse. Does this mean that they will recover just as strongly in a GE? No. Will even the patterns on display in the results, both in specific councils and aggregated nationally, necessarily be reflected at the next GE? No. The results tell us about today, not tomorrow.
This is definitely true for two main reasons. Firstly there are an awful lot of people that would vote Lib Dem locally that wouldn't nationally because in many areas the Lib Dems campaign a quasi-independents talking only about local issues and not about national ones (this is probably how they swept Chelmsford Council for example). Secondly general elections have much higher turnout than local elections and the types of people who don't bother to vote in local elections but do in general elections are disproportionately unlikely to vote Lib Dem (or Green for that matter) as most will vote for their government preference i.e. Conservative or Labour.
Still a good set of elections for the Lib Dems albeit from a low base. Arguably they deserved a good year after nearly a decade of dreadful or disappointing results.