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> it might make sense to borrow 900 in ETH with 1000 ETH collateral. Then you make your vote on the DAO with a power of 1900

No, you would vote on the DAO with a power of 900, because your original 1000 ETH collateral is being held by the lending protocol

Not necessarily. There are mulitple ways it could work.

Two examples:

The DAO could support the lending protocol. Counting your assets in the lending protocol towards your voting power.

The lending protocol could support the DAO. Not allowing you to withdraw you collateral but allowing you to signal something to the DAO.