These are so far the best open source lightning wallets that I've found which don't force you to use the Play Store to install them:
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Blixt Wallet. This is a really nice and modern lightning wallet. It has a lot of state of the art features like Keysend, Lightning Address, LNURL and WebLN. They use LND and Neutrino directly on the phone. They have the apk download available from github releases.
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SBW. Simple Bitcoin Wallet. This is a great non-custodial lightning wallet. It's very simple to use, you can send and receive bitcoin on-chain and through lighting by just scanning a QR code or pasting an invoice. It's based on Immortan, a custom implementation of lightning for light nodes. They also offer optional services like lightning channels through partners if you don't have your own node. It's available from f-droid, and github releases.
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Breez. A great open source, non-custodial, lnd and neutrino based lightning wallet with a lot of features like automatically opening channels for you. You can get the apk from the github releases.
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Phoenix. A lightning wallet based on Eclair. This wallet provides a great user experience, and channels are managed for you. You can get the apk from the github releases.
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BlueWallet. This is a great wallet with a lot of functionality. It's been around for a few years already, and it keeps getting better. You can either use your own lightning node or one of the nodes they provide for you. It's available from f-droid and github releases.
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Zeus. This is a great wallet for lightning node operators. You can send and receive Bitcoin through lightning or on-chain. It provides a direct connection to your node where you can manage all the details of its operation. It works for lnd, Eclair, and c-lightning nodes. You can get it from f-droid and github releases.
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Muun. Muun is also a great and simple lightning wallet, and it's open source, but they don't publish their apk directly anywhere other than the Play Store. Here's a discussion about it. You can get the apk, but it's more complicated. Also, note that they do require Google Play Services running on the phone to use it.