Nevir was was a competent and prolific manufacturer, if the number & quality of pieces I've seen by him are any guide.
Yes, I'm sure that the "L" is an assayer's letter. Around the middle of the 18th century, the Berlin guild began putting a letter in the city mark to identify the tenure of the guild warden, beginning with "A". The ranges of the earlier letters are known only from dated items:
A = Items dated 1747 - 1757
B = Late 1750s - early 1760s?
C = Items dated 1763 — 1772*
D = Items dated 1770* - 1776
E = Items dated 1776 - 1777
F = Items dated 1779 — 1785
(*probably an anomaly on a pre- or post-dated item; it seems certain that the letters did not overlap)
The names and tenures of later wardens are known:
G = F. J. Stoltz, 1786 - 1803
H = C. G. Pintsch, 1803 - 1817
I = H. W. Zarnack, 1817 - 1818
From 1819, Berlin pieces were marked with two assayer's letters: that of the warden, which continued to appear in the punch with the bear, and that of the secondary assayer, which appeared by itself. The names & dates become muddied once again after the abrogation of the guild's authority around 1864.
Warden’s marks (with the bear)
K = J. C. S. Kessner, 1819 — 1854
L = J.W. D. Friedrich, 1854 - 1863
M = Unknown, ca. 1863 — ca. 1869
N = Unknown, ca. 1870 — 1882
Secondary Assayer’s marks (standing alone)
A = B. G. F. Andreack, 1819 — 1842
B = Ch. F. Deppe, 1842 — 1847
C = J. W. D. Friedrich, 1848 - 1854
D = L. Th. Wendelboe, 1854 - ca. 1864
E = Unknown, ca. 1864 — ca 1868
F = Unknown, ca. 1868 — ca. 1875
G = Unknown, ca. 1875 — ca. 1882
The overlap in these later marks can help narrow the dating a little; I’ve recorded the primary/secondary assayer’s letters in the following combinations:
K/A = 1819 — 1842
K/B = 1842 — 1847
K/C = 1848 — 1854
L/C = 1854
L/D = 1854 — 1863
M/E = ca. 1863 — ca. 1869
N/F = ca. 1870 - ca. 1875
N/G = ca. 1875 — ca. 1882
I notice that your item doesn’t have the secondary assayer’s mark; at least you haven't shown it. This is unusual but not unprecedented; you do from time to time see post-1819 pieces with just one of the two required marks.
The vast majority of this information is from Wolfgang Scheffler’s Berliner Goldschmiede, still the standard reference for Berlin silver. It could well use an update, though; I’ve come across many maker’s marks not in illustrated it, and I wonder if any better information on the early and later warden’s marks have come to light in the 40 years since it was published.