Can the word “encore” be used to refer to a context outside the entertainment sector ? Is it perfectly correct to be used in academia for example?

Its usage is certainly more common in the entertainment sector but in that example the content and intent is clear; this is independent of whether a lecture is considered a performance.

To "deliver an encore" as meaning "more of the same" could be used elsewhere, often in the negative form to describe a repetition not occurring e.g. an encore not taking place meaning a sports team not winning back-to-back games.

Merriam-Webster's Eleventh Collegiate Dictionary (2003) gives one reasonably audience-free definition of encore as a noun (definition 2b below):

1: a demand for repetition or reappearance made by an audience 2a: a reappearance or additional performance demanded by an audience b: a second achievement esp. that surpasses the first

Meaning 2b applies to instances like this one: In 2004, after painstaking effort, Russian and U.S. scientists succeed in briefly synthesizing ununpentium. A friend of one of the scientists asks, "What are you going to do for an encore?" The figurative reference is to performing before an audience, but the question itself is about topping a remarkable achievement.

"The lecturer gave an encore presentation" sounds fine to me, by the way. Google Ngram Viewer results find the phrase "encore performance" as far back as the 1870s. A typical example (from 1892):

We spoke before of the great and instantaneous success Miss Aus der Ohe achieved with the large audience, and after a triple most hearty recall she sat down to play as an encore performance Liszt's E major polonaise.

In such phrases, encore functions as an adjective and simply means "repeat." Merriam-Webster's doesn't endorse encore as an adjective, but that doesn't mean that people don't commonly use it as one, at least in the United States.

FOLLOW-UP (June 5, 2013): As for the history of "encore presentation," the phrase seems to have become fairly well established by the 1970s: Google Ngram Viewer search results return at least 18 unique instances of it between 1966 and 1979 in published works. The three earliest instances that Ngram Viewer finds date to 1946, 1955, and 1962.

From Bookbinding & Book Production, Volume 43 (1946):

H. Wolff's entry this year was another of its useful and attractively produced desk pads, while American Book-Stratford Press pleased friends with an encore presentation of its leatherbound pocket memo book.

From Musical Courier, Volumes 151–152 (1955):

The Co-Opera Company, a young group that presents one-act operas in English, in the round, gave an encore presentation of Arthur Benjamin's Prima Donna, in plot and score one of the finest of contemporary comedy operas.

From Autoharp, Issues 11–20 (1962):

Her encore presentation of the lullaby, Rozhinkes and Mendlen (Raisins and Almonds), was as tender a moment as any musical student could ever hope to hear, while her minor-key renditions of songs of Jewish family life brought back a dead age better than the books and ethnographic studies can ever hope to equal.

FURTHER FOLLOW-UP (also June 5, 2013): In the period from 1969 to 1979, "encore presentation" came into more frequent use in connection with lectures, seminars, and public addresses. Ngram Viewer notes the following instances:

"Adding up the results after the last of the 240 visitors had left, Friden [a manufacturer of electronic calculators] officials said the $46,500 in immediate and projected sales justified an encore presentation" [International Commerce, August 24, 1970].

"An encore presentation will be held at the New York Hilton on Monday, October 18th, again featuring speakers with varying points of view, a probing press panel and topics of current interest." (FACS Forum, 1975).

"Next month, an NPL encore presentation will entertain Van Camp brokers vacationing at company expense on the isle of Martinique." (The Executive of Los Angeles, 1978 {cited text not visible in snippet window}).

"A private trade show in the trucking industry, the Mack Trucks 'Super Spectacular,' was a success in its encore presentation in the New Orleans Superdome" (Industrial Marketing, 1979).

"The seminar, an encore presentation from Chicago's June CES, drew enthusiastic response when Berman pointed out weak, self-defeating sales practices and the overuse of the phrase 'Can I help you?'" (Billboard, January 27, 1979).

The most common circumstance where "encore presentation" appears during the 1970s is in connection with repeat showings of TV shoes, as in this instance from United Methodists Today (1974):

April 12 on ABC, 10-11 p.m. Encore presentation of A Man Named John, starring Raymond Burr and based on the life of Archbishop Angelo Roncalli, later to become Pope John XXIII.

Evidently, broadcasters decided that "encore presentation" would sound more appealing to potential viewers than "rerun."

Ngram Viewer didn't return any matches for "encore lecture," "encore demonstration," "encore address," or "encore seminar," suggesting that few encore + noun combinations are in common use in publishing. However, it did find quite a few for "encore appearance," from as far back as 1927.

FURTHER FURTHER FOLLOW-UP (July 31, 2021): Looking again at Google Books search results, I found a figurative instance of "encore performance" from the early twentieth century. From "A Day's Jack Fishing" in Baily's Magazine of Sports and Pastimes (March 1908), a vignette in which a little boy who can't swim has been forced to climb a tree overhanging a pond to retrieve some fishing bait that had got hung up in the branches by an inept (but intimidating) angler:

When he [the boy] got down again, he looked from the shilling in his grimy little fist to the Major, and then at the shilling again, and sped off, making a bee-line for the farm, as fast as his legs could carry him. He evidently did not want an encore performance.

An even earlier instance, in which "encore performance" appears in the context of rereading an address originally given at some previous professional gathering, occurs in Henry McManus, "Thoughts About Inlays," a paper read before the Vermont State Dental Society at its twenty-eighth annual meeting, March 18–18, 1904, reprinted in The Dental Brief (November 1904):

In accepting the kind invitation of your very worthy secretary to supplement the clinic I hope to have the pleasure of giving later in the session, with a paper, I want to state positively that I did not comply with his flattering suggestion that I, like the learned lights of our profession, could reach down into the bottom drawer and find a paper suitable for any occasion and allow it an encore performance here.