Lightning node on a Bitcoin SPV
LND is experimenting with the new Neutrino BIP157-style SPV at the moment. Check out their repo for news. 

Both Bitcoin Lightning Wallet and Eclair on Android use a trusted server for syncing with the network.

BIP-37-style SPV is not a good choice for anyone (because of privacy issues), but particularly not for Lightning wallets, because it is very easy for an adversary to help a channel partner in cheating by withholding critical transactions that your wallet would have to respond to.