We should have a way of monitoring the age of OSM data. This will show problems with consuming updates. An example graph of this is on OpenStreetMap munin
Although strictly speaking the lag is the difference between the local data timestamp and the planet.osm.org timestamp, it's common to just assume the planet.osm.org timestamp is the current time, avoiding the need to request it while monitoring. This has a maximum error of one minute, unless there are upstream problems.
The common way to do this is with https://github.com/openstreetmap/mod_tile/blob/master/munin/replication_delay. It wouldn't port directly to our monitoring, but there's nothing complicated there.