The payment channel network aims to solve the problems of long payment confirmation time and limited throughput in cryptocurrencies through off-chain payments. Hash Time-Lock Contract (HTLC) is an off-chain payment protocol that Lightning Network (LN) adopted. Unfortunately, when performing high-valued payments off-chain, due to the impact of payment channel capacity, it is often necessary to split a single payment, which increases the transaction fees and time. Therefore, we propose LightPay, an atomic off-chain multi-path payment protocol based on adapter signature and discrete logarithm problem. Among different conditions encoded in the multi-path contract, the multi-path transmission of a single high-valued payment can be realized under the premise of the unlinkability of partial payments. We construct an ideal functionality in the Universal Composability framework and demonstrate that LightPay UC-realizes it, thereby providing proof of its security and privacy. Experimental results indicate that the payment success rate of LightPay can be increased by 11.08% in 0.0025 BTC payments compared with the single-path payment protocol Multihop HTLC in LN. Additionally, compared with the multi-path payment protocol CryptoMaze, the communication overhead required by LightPay is reduced to about 55.6% on average in the simulated network. Overall, LightPay has advantages regarding payment success rate and overhead.