systems/lcm: Re-enable lcm_interface_system_test

The test conditions have been relaxed to account for an (purposeful)
race condition with the transmitter thread.

Testing with --runs_per_test=50 reliably trips the failure on master,
and does not trip the failure after this fix.

systems/lcm/BUILD.bazel

@@ -200,8 +200,6 @@ drake_cc_library(
 
 drake_cc_googletest(
     name = "lcm_interface_system_test",
-    # TODO(jwnimmer-tri) Re-enable this after fixing the race condition.
-    tags = ["manual"],
     deps = [
         ":lcm_interface_system",
         ":lcm_subscriber_system",

systems/lcm/test/lcm_interface_system_test.cc

@@ -103,6 +103,11 @@ TEST_P(LcmInterfaceSystemTest, AcceptanceTest) {
     // still publish and service subscriptions.  The LcmSubscriberSystem's
     // subscriptions should NOT be called anymore.
     simulator.reset();
+    // Empty the queue of anything that was published subsequent to the final
+    // simulator.AdvanceTo call, but prior to the simulator.reset call.
+    drake_lcm->HandleSubscriptions(0);
+    // Even though the transmit thread is still publishing, nothing else should
+    // appear at the handlers because there are no more active subscriptions.
     int total = 0;
     for (int i = 0; i < 100; ++i) {
       total += drake_lcm->HandleSubscriptions(1);