In the OP it says that LND supports neutrino, but I have no idea what is it
Neutrino is a Bitcoin light-client. Its
Github page states that it still should not be used on the mainnet.
Is there any tutorial that explains how I'll setup my LN node without running a Bitcoin node?
You need a Bitcoin node. Your Lightning Network node needs to constantly monitor the mempool and the blockchain. Otherwise, it would not be able to tell when it's safe to use a specific channel or if any of your peers is trying to cheat. It also needs to know what fees are reasonable at the moment so that a commitment transaction could be confirmed quickly.
You should be able to use a pruned node with c-lightning without any extra setup. Keep in mind the following.
You can use a pruned node if you choose either c-lighting or LND. However, whichever you choose, you need to be careful about the discrepancy in the reported blockheight by your Bitcoin and Lightning nodes. If your Lightning node crashes for some reason and your Bitcoin node prunes a block which has not been processed yet by the other node then your Lightning node will get stuck. See the following links for more information (
#1,
#2).