You don't need to beat Lambda again to start a New Game+, you just pick it right in Title Screen and it doesn't matter where you are in the cleared file.
That said there's a good deal of post-game content back in the main game after beating Future Arc. So I don't recommend starting a NG+ until you're ready for a 60-sec trophy run unless you'd much rather do all the extra stuff (i.e. hidden bosses, Zhonecage) with all the enhancements from the Grade Shop.
If you're confused by all of this, just save on a separate file after beating Lambda for the first time and load it, you'll see what happens.
(BTW SHINE, this is the same in Vesperia, saving after beating the final boss and then loading it won't put you in a New Game+, you start that in the Title Screen as well)
--
http://img.imgcake.com/whitelens/MadokaMagicaMessagejpguj.jpg
http://img.imgcake.com/whitelens/MadokaThanksjpgen.jpg