diff --git a/pkg/crosscluster/logical/lww_row_processor.go b/pkg/crosscluster/logical/lww_row_processor.go
index d9818d3ee050..468fa3bcf065 100644
--- a/pkg/crosscluster/logical/lww_row_processor.go
+++ b/pkg/crosscluster/logical/lww_row_processor.go
@@ -15,6 +15,7 @@ import (
 	"github.com/cockroachdb/cockroach/pkg/jobs/jobspb"
 	"github.com/cockroachdb/cockroach/pkg/keys"
 	"github.com/cockroachdb/cockroach/pkg/kv"
+	"github.com/cockroachdb/cockroach/pkg/kv/kvpb"
 	"github.com/cockroachdb/cockroach/pkg/repstream/streampb"
 	"github.com/cockroachdb/cockroach/pkg/roachpb"
 	"github.com/cockroachdb/cockroach/pkg/settings"
@@ -80,6 +81,15 @@ type querier interface {
 	RequiresParsedBeforeRow(catid.DescID) bool
 }
 
+// isLwwLoser returns true if the error is a ConditionFailedError with an
+// OriginTimestampOlderThan set.
+func isLwwLoser(err error) bool {
+	if condErr := (*kvpb.ConditionFailedError)(nil); errors.As(err, &condErr) {
+		return condErr.OriginTimestampOlderThan.IsSet()
+	}
+	return false
+}
+
 type queryBuilder struct {
 	// stmts are parsed SQL statements. They should have the same number
 	// of inputs.
@@ -592,6 +602,9 @@ func (lww *lwwQuerier) InsertRow(
 			sess.QualityOfService = nil
 		}
 		if _, err = ie.ExecParsed(ctx, replicatedOptimisticInsertOpName, kvTxn, sess, stmt, datums...); err != nil {
+			if isLwwLoser(err) {
+				return batchStats{}, nil
+			}
 			// If the optimistic insert failed with unique violation, we have to
 			// fall back to the pessimistic path. If we got a different error,
 			// then we bail completely.
@@ -615,7 +628,11 @@ func (lww *lwwQuerier) InsertRow(
 		sess.QualityOfService = nil
 	}
 	sess.OriginTimestampForLogicalDataReplication = row.MvccTimestamp
-	if _, err = ie.ExecParsed(ctx, replicatedInsertOpName, kvTxn, sess, stmt, datums...); err != nil {
+	_, err = ie.ExecParsed(ctx, replicatedInsertOpName, kvTxn, sess, stmt, datums...)
+	if isLwwLoser(err) {
+		return batchStats{}, nil
+	}
+	if err != nil {
 		log.Warningf(ctx, "replicated insert failed (query: %s): %s", stmt.SQL, err.Error())
 		return batchStats{}, err
 	}
diff --git a/pkg/crosscluster/logical/lww_row_processor_test.go b/pkg/crosscluster/logical/lww_row_processor_test.go
index e9d6af36053f..7de87aac296f 100644
--- a/pkg/crosscluster/logical/lww_row_processor_test.go
+++ b/pkg/crosscluster/logical/lww_row_processor_test.go
@@ -459,9 +459,6 @@ func TestLWWConflictResolution(t *testing.T) {
 				runner.CheckQueryResults(t, fmt.Sprintf("SELECT * from %s", tableNameDst), expectedRows)
 			})
 			t.Run("cross-cluster-local-delete", func(t *testing.T) {
-				if !useKVProc {
-					skip.IgnoreLint(t, "local delete ordering is not handled correctly by the SQL processor")
-				}
 				tableNameDst, rp, encoder := setup(t, useKVProc)
 
 				runner.Exec(t, fmt.Sprintf("INSERT INTO %s VALUES ($1, $2)", tableNameDst), row1...)
@@ -507,9 +504,6 @@ func TestLWWConflictResolution(t *testing.T) {
 				runner.CheckQueryResults(t, fmt.Sprintf("SELECT * from %s", tableNameDst), expectedRows)
 			})
 			t.Run("remote-delete-after-local-delete", func(t *testing.T) {
-				if !useKVProc {
-					skip.IgnoreLint(t, "local delete ordering is not handled correctly by the SQL processor")
-				}
 				tableNameDst, rp, encoder := setup(t, useKVProc)
 
 				runner.Exec(t, fmt.Sprintf("INSERT INTO %s VALUES ($1, $2)", tableNameDst), row1...)
diff --git a/pkg/sql/row/errors.go b/pkg/sql/row/errors.go
index a7e856303a32..db584232c547 100644
--- a/pkg/sql/row/errors.go
+++ b/pkg/sql/row/errors.go
@@ -41,6 +41,11 @@ func ConvertBatchError(ctx context.Context, tableDesc catalog.TableDescriptor, b
 		)
 
 	case *kvpb.ConditionFailedError:
+		if !v.OriginTimestampOlderThan.IsEmpty() {
+			// NOTE: we return the go error here because this error should never be
+			// communicated to pgwire. It's exposed for the LDR writer.
+			return origPErr.GoError()
+		}
 		if origPErr.Index == nil {
 			break
 		}