Lightning has two main applications - every day payments and adding privacy to your BTC funds. Neither of them implies storing it for long time without using. In first case you use it every day and notice a malicious force close (which my node which is not small detected only one time during several years and it was a mistake, not a malicious action). In the second case you open a channel, tunnel the funds through the network and you are done - you store new unrelated coins onchain for long time.
Hiding IP is a separate task. You can do it on your own, LND and bitcoind both support working behind Tor and using onion sites for incoming connections.
Regarding using closed source apps, it is not because of lightning. Majority stores other cryptos on centralised exchanges. It happens, because it is beneficial for the custodians who get all the coins, so they can invest into development and promotion of their products. While Devs of self-custody wallets, e.g. Simple Bitcoin Wallet, receive small funding and can not promote as aggressively as big guys do.