Even though “lecturership” is more logical (being analogous to “professorship” and “ambassadorship,” for example), it hasn’t established itself as a standard term. The usual word is the age-old “lectureship,” which is now about 100 times as common in print sources — e.g.: “His extracurricular activities include guest lectureships at Juilliard and charities like Paul Newman’s Hole in the Wall Camp for seriously ill children.” Joe Williams, “Busy Kevin Kline Makes Time for His Hometown,” St. Louis Post-Dispatch, 22 Nov. 2002, Mag. Section, at F1.
Those who write “lecturership” — and today it is mostly confined to British English — are likely to be thought pretentious.
The following sentence suggests, no doubt unwittingly, that Oxford is a more pretentious place than Liverpool: “After a lecturership [read ‘lectureship‘] at Merton College, Oxford, and an assistant lectureship at Liverpool University, Roberts was elected, aged 26, Professor of History at the Rhodes University College.” “Obituary of Professor Michael Roberts,” Daily Telegraph, 25 Jan. 1997, at 13.
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Quotation of the Day: “Often the bright lexicon of one’s youth tends to exert an umbilical pull through life. Many a man who has lost his dictionary or worn it to tatters will set out to buy the same one all over again, in the identical edition, if possible; a new type face in his dictionary would be as unsettling to him as a new type of face on his father or mother — probably because, in these uncertain times, so many people look confidently to the dictionary as the last stronghold of immutable authority.” Felicia Lamport, “Dictionaries: Our Language Right or Wrong” (1950), in Words, Words, Words About Dictionaries 64 (Jack C. Gray ed., 1963).