As far as I know, Dapps provide more complex functionalities than Lapps. However, Lapps are much better than Dapps simply because they're instant with very low fees. From what I've seen, there are many Lapps which provide the same features as traditional Dapps of today such as online casinos, lotteries, and even exchanges. But this is still relatively new, as the Lightning Network is not ready for mainstream deployment. Lightning-apps (Lapps) could be a real game changer if adopted by people in mass because of its true benefits relative to Dapps.
Still though, Dapps might remain as the "standard" for decentralized Blockchain applications within the mainstream world. Lapps may bring convenience but they're not as secure or reliable as Dapps. It's no wonder why many people still use the Ethereum blockchain for smart-contract interaction (despite its slow speeds and high fees). In the end, people will choose among different types of apps within the mainstream world. If you want true smart-contract functionality, then Ethereum would be the way to go. Most recently, a Bitcoin sidechain emerged named "Rootstock" which provides the same functionalities for Dapps as Ethereum but with the security of the Bitcoin blockchain.
Without a doubt, Lapps are much easier to develop than Dapps. But as I've said before, they're still in their infancy. An extensive list of Lapps can be found here. Hopefully, we'd get to see more Lapps as people adopt Bitcoin's Lightning Network within the mainstream world. Just my thoughts