Can TiKV Importer be restarted while TiDB Lightning is running?

No. TiKV Importer stores some information of engines in memory. If tikv-importer is restarted, tidb-lightning will be stopped due to lost connection. At this point, you need to destroy the failed checkpoints as those TiKV Importer-specific information is lost. You can restart TiDB Lightning afterwards.

See also How to properly restart TiDB Lightning? for the correct sequence.