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 (ShutdownRequested()) {
        LogPrintf("Shutdown requested. Exiting.\n");
        return false;
    }
    ChainstateManager& chainman = *Assert(node.chainman);
    assert(!node.peerman);
    node.peerman = PeerManager::make(*node.connman, *node.addrman, node.banman.get(),
                                     chainman, *node.mempool, ignores_incoming_txs);
    RegisterValidationInterface(node.peerman.get());
     ***
     If reindex-chainstate was specified, delay syncing indexes until ThreadImport has reindexed the chain
    if (!fReindexChainState) g_indexes_ready_to_sync = true;
    if (args.GetBoolArg("-txindex", DEFAULT_TXINDEX)) {
        auto result{WITH_LOCK(cs_main, return CheckLegacyTxindex(*Assert(chainman.m_blockman.m_block_tree_db)))};
        if (!result) {
            return InitError(util::ErrorString(result));
        }
        g_txindex = std::make_unique<TxIndex>(interfaces::MakeChain(node), cache_sizes.tx_index, false, fReindex);
        if (!g_txindex->Start()) {
            return false;
        }
    }
    for (const auto& filter_type : g_enabled_filter_types) {
        InitBlockFilterIndex([&]{ return interfaces::MakeChain(node); }, filter_type, cache_sizes.filter_index, false, fReindex);
        if (!GetBlockFilterIndex(filter_type)->Start()) {
            return false;