The crown above the L is clearly a royal crown or grand duke's crown.
In all ruling houses, only the first name(s) were used in abbreviated form in the monogram.
In Springer's ledgers it says: "delivered to crown prince Prince Leopold".
The monogram on the gun corresponds to the monograms of Ludwig I and Ludwig II of Bavaria. It was probably also that of Leopold of Bavaria. They belonged to the house of Wittelsbach:
Correspondence Map of Ludwig II:
Even the high nobility did not only carry magnificent guns. On the contrary, the real hunters among them often preferred good utility weapons. A good example is the Ischler Stutzen of the Austrian Emperor Franz Joseph, built by the Ferlach gunsmith Fanzoj.
Cheers,
Wolfgang