After conversation on irc it appears there's some cases where Bitcoin core will serve feerate information even though it loaded a fairly old fee estimates file and is still syncing the chain. This is pretty dangerous for lightning nodes, at least on legacy channels or pre-package-relay.

The immediate improvement would be to store fee estimates to disk once an hour or so to reduce the chance of having an old file. From there this case could probably be detected and refuse to serve estimates until we sync.
if (!CheckDiskSpace(args.GetDataDirNet())) {
        InitError(strprintf(_("Error: Disk space is low for %s"), fs::quoted(fs::PathToString(args.GetDataDirNet()))));
        return false;
    }
    if (!CheckDiskSpace(args.GetBlocksDirPath())) {
        InitError(strprintf(_("Error: Disk space is low for %s"), fs::quoted(fs::PathToString(args.GetBlocksDirPath()))));
        return false;
    }
    int chain_active_height = WITH_LOCK(cs_main, return chainman.ActiveChain().Height());
     On first startup, warn on low block storage space
    if (!fReindex && !fReindexChainState && chain_active_height <= 1) {
        uint64_t assumed_chain_bytes{chainparams.AssumedBlockchainSize() * 1024 * 1024 * 1024};
        uint64_t additional_bytes_needed{
            chainman.m_blockman.IsPruneMode() ?
                std::min(chainman.m_blockman.GetPruneTarget(), assumed_chain_bytes) :
                assumed_chain_bytes};
        if (!CheckDiskSpace(args.GetBlocksDirPath(), additional_bytes_needed)) {
            InitWarning(strprintf(_(
                    "Disk space for %s may not accommodate the block files. " \
                    "Approximately %u GB of data will be stored in this directory."
                ),
                fs::quoted(fs::PathToString(args.GetBlocksDirPath())),
                chainparams.AssumedBlockchainSize()
            ));
        }
    }
     Either install a handler to notify us when genesis activates, or set fHaveGenesis directly.
     No locking, as this happens before any background thread is started.
    boost::signals2::connection block_notify_genesis_wait_connection;
    if (WITH_LOCK(chainman.GetMutex(), return chainman.ActiveChain().Tip() == nullptr)) {