The Collaborative International Dictionary of English v.0.48:

Mesne \Mesne\, a. [Cf. Mean intermediate.] (Law)
   Middle; intervening; as, a mesne lord, that is, a lord who
   holds land of a superior, but grants a part of it to another
   person, in which case he is a tenant to the superior, but
   lord or superior to the second grantee, and hence is called
   the mesne lord.
   [1913 Webster]

   Mesne process, intermediate process; process intervening
      between the beginning and end of a suit, sometimes
      understood to be the whole process preceding the
      execution. --Blackstone. --Burrill.

   Mesne profits, profits of premises during the time the
      owner has been wrongfully kept out of the possession of
      his estate. --Burrill.
      [1913 Webster] Meso

Bouvier's Law Dictionary, Revised 6th Ed (1856):

MESNE. The middle between two extremes, that part between the commencement
and the end, as it relates to time.
     2. Hence the profits which a man receives between disseisin and
recovery of lands are called mesne profits. (q.v.) Process which is issued
in a suit between the original and final process, is called mesne process.
(q.v.)
     3. In England, the word mesne also applies to a dignity: those persons
who hold lordships or manors of some superior who is called lord paramount,
and grant the same to inferior persons, are called mesne lords.



Bouvier's Law Dictionary, Revised 6th Ed (1856):

MESNE, WRIT of. The name of an ancient writ, which lies when: the lord
paramount distrains on the tenant paravail; the latter shall have a writ of
mesne against the lord who is mesne. F. N. B. 316.