itest: add payment test with max htlc restriction

diff --git a/itest/list_on_test.go b/itest/list_on_test.go
index 851662f..7f9eaf5 100644
--- a/itest/list_on_test.go
+++ b/itest/list_on_test.go
@@ -242,6 +242,10 @@ var allTestCases = []*lntest.TestCase{
 		Name:     "wumbo channels",
 		TestFunc: testWumboChannels,
 	},
+	{
+		Name:     "max htlc path payment",
+		TestFunc: testMaxHtlcPathPayment,
+	},
 	{
 		Name:     "max htlc pathfind",
 		TestFunc: testMaxHtlcPathfind,
diff --git a/itest/lnd_max_htlc_path_test.go b/itest/lnd_max_htlc_path_test.go
new file mode 100644
index 0000000..3e8db16
--- /dev/null
+++ b/itest/lnd_max_htlc_path_test.go
@@ -0,0 +1,74 @@
+package itest
+
+import (
+	"github.com/lightningnetwork/lnd/lnrpc"
+	"github.com/lightningnetwork/lnd/lnrpc/routerrpc"
+	"github.com/lightningnetwork/lnd/lntest"
+)
+
+// testMaxHtlcPathPayment tests that when a payment is attempted, the path
+// finding logic correctly takes into account the max_htlc value of the first
+// channel.
+func testMaxHtlcPathPayment(ht *lntest.HarnessTest) {
+	// Create a channel Alice->Bob.
+	chanPoints, nodes := ht.CreateSimpleNetwork(
+		[][]string{nil, nil}, lntest.OpenChannelParams{
+			Amt: 1000000,
+		},
+	)
+	alice, bob := nodes[0], nodes[1]
+	chanPoint := chanPoints[0]
+
+	// Alice and Bob should have one channel open with each other now.
+	ht.AssertNodeNumChannels(alice, 1)
+	ht.AssertNodeNumChannels(bob, 1)
+
+	// Define a max_htlc value that is lower than the default.
+	const (
+		maxHtlcMsat   = 50000000
+		minHtlcMsat   = 1000
+		timeLockDelta = 80
+		baseFeeMsat   = 0
+		feeRate       = 0
+	)
+
+	// Update Alice's channel policy to set the new max_htlc value.
+	req := &lnrpc.PolicyUpdateRequest{
+		Scope: &lnrpc.PolicyUpdateRequest_ChanPoint{
+			ChanPoint: chanPoint,
+		},
+		MaxHtlcMsat:   maxHtlcMsat,
+		MinHtlcMsat:   minHtlcMsat,
+		BaseFeeMsat:   baseFeeMsat,
+		FeeRate:       feeRate,
+		TimeLockDelta: timeLockDelta,
+	}
+	alice.RPC.UpdateChannelPolicy(req)
+
+	expectedPolicy := &lnrpc.RoutingPolicy{
+		FeeBaseMsat:      baseFeeMsat,
+		FeeRateMilliMsat: feeRate,
+		TimeLockDelta:    timeLockDelta,
+		MinHtlc:          minHtlcMsat,
+		MaxHtlcMsat:      maxHtlcMsat,
+	}
+
+	// Wait for the policy update to propagate to Bob.
+	ht.AssertChannelPolicyUpdate(
+		bob, alice, expectedPolicy, chanPoint, false,
+	)
+
+	// Create an invoice for an amount greater than the max htlc value.
+	invoiceAmt := int64(maxHtlcMsat + 10_000_000)
+	invoice := &lnrpc.Invoice{ValueMsat: invoiceAmt}
+	resp := bob.RPC.AddInvoice(invoice)
+
+	// Attempt to pay the invoice from Alice. The payment should be
+	// splitted into two parts, one for the max_htlc value and one for the
+	// remaining amount and succeed.
+	payReq := &routerrpc.SendPaymentRequest{
+		PaymentRequest: resp.PaymentRequest,
+		FeeLimitMsat:   noFeeLimitMsat,
+	}
+	ht.SendPaymentAssertSettled(alice, payReq)
+}