AAC is supported for playback, but it's not being used as codec for A2DP in AOSP ROMs or even the stock Nexus ROMs. Two very different things. I wish there was a way to at least enable AAC for A2DP without too much effort.
There's also no such thing as lossless AAC, you probably mean Apple Lossless (ALAC).
I just recently got into this whole topic with apt-x and stuff, since I discovered that headsets like the Samsung HS3000 or the new "audiophile" Noble BTS (it's not so audiophile at all and not worth the money, I wish I had looked it up on HeadFi or similar before I bought one). The chip in the BTS is from CSR and also supports MP3 and AAC over A2DP. I'm on stock 5.1.1 with my Nexus 4 and it's just using SBC, unfortunately. But at least at the highest quality setting (the bitpool 53 thing, which equals 328 kbps). I'd still prefer AAC, which should be possible - doesn't Android always include an AAC encoder, for video recording and stuff?
By the way, it took me a while to find this when I was asking myself how to find out, which codec my devices were actually using when paired. I found a very convenient (even for noobs) solution, so in case it's not already known to most interested people here, I'll just leave this here for reference as well: It's the answer at the bottom on that page
https://android.stackexchange.com/q...p-codecs-my-phone-supports-is-currently-using
It's really simple: All you need is debug mode and the Bluetooth HCI-snooping setting enabled. Then you pair your bluetooth device, play a bit of audio, then pull the /sdcard/btsnoop_hci.log and open it in Wireshark. Then you can search for "codec" and you'll find various packets, showing which codec and settings are being used.