The answer to the question "Is a valid Eucharist dependent on a valid priesthood?" is emphatically Yes, because the priest who offers the Eucharist is our Lord Jesus Christ. His "orders" are perfectly valid. The pastor stands in the place of Christ and celebrates in His stead and by His command.
Ordination confers the right and duty to stand in the place of Christ at the altar, not the "power" to confect the Eucharist. That power belongs always and only to Christ. This prayer (though it is Orthodox, not Lutheran) says it well:
Enable me by the power of Thy Holy Spirit so that, being vested with the grace of priesthood, I may stand before Thy holy Table and celebrate the mystery of Thy holy and pure Body and Thy precious Blood ... for Thou, O Christ our God, art the Offerer and Thou art the One offered; it is Thou Who receivest the offering and Thou art Thyself the offering which is distributed.
If a lay person presumes to stand in the place of Christ at the altar, the difficulty is not that he does not have the "power to confect" (which a properly ordained priest does not have either); it is that he has presumed to stand in Christ's place when he has not been called to do so. The faithful ought always to be able to be confident that the celebrant does, in fact, stand in the place of Christ. When a lay person, absent a proper call to that role, presumes to celebrate, the faithful cannot have that confidence.
Did I answer rightly?