Our priest will be away on January 13. We plan Reader's Services for that day as we have done on similar occasions. Yes, a layman can read the Gospel when no clergy are present to do so (at least in the Typika service as we do it), but it, like the Epistle, is read in a plain speaking voice and without the usual responses.
We've even had a couple of times when we've done a reader's service when the priest is in the building but unable to participate. This has happened at Orthros when the priest has arrived late and has all the preparations to do for the Divine Liturgy that will follow. No Gospel reading in that case.