TL;DR 1902

Well the concept as we know it was first elucidated by Friedrich Ratzel in the last decade of the 19th century. He expanded on these writings in the 1897 publication Political Geography and the 1901 essay Der Lebensraum.

A quick search of JSTOR suggests that the terms first entered English language scholarship via reviews of the above. The oldest example I could find came from the Journal of Political Economy, Vol. 10, No. 2 (Mar., 1902) in the form of two reviews by William Scott and G. Cassel of Festgaben für Albert Schäffle zur siebenzigsten Wiederkehr seines Geburtstages, the work in which Ratzel's essay cited above first appears. Unfortunately, neither of the reviewers discussed the specific essay by Ratzel, although Scott does state, "The monographs contained in this book cannot be regarded as important contributions to knowledge."

There is a third review, from Political Science Quarterly, Vol. 17, No. 4 (Dec., 1902) by Ernest Bogart which goes slightly more in depth. Since Jstor is behind a pay wall, and I'm not entirely sure how much of the review will be open to the public, I'll quote the relevant portion here:

In the second article, Professor Friedrich Ratzel has made an interesting, bio-geographical study, entitled " Der Lebensraum." The distinguishing characteristic of life, he says, is its conquest of room or space, which is aided by winds and streams and currents and larger animals. But these massive means of migration are less important than Darwin would have us believe; far more important is what Ratzel calls colonization -" the people, the race, the species, can migrate only by colonizing." At the same time with the movement of all life there goes on a struggle for space -this is really the so-called struggle for existence. In view of these facts, how are we to determine the "creation centre" of a species? The widespread belief that the point of origin of a species corresponds with the centre of its geographical distribution, is false. The periphery is of more importance than the centre, for that may indicate the direction in which the migration and colonization have been proceeding, and from this we may guess at the point of origin. But a guess is all we are entitled to.

While I cannot prove that English language scholarship never dealt with the term before these instances, my best guess is that these are the earliest references to it. So your date, depending on how in depth a discussion you're looking for is either March 1902 or December 1902.