Simple answer.. no, it's not a period coat that I am familiar with. I looked up coats for Lancers in the 1900 Officers' Dress Regulations which is usually a source of instant answers. However, in this case, it is not very helpful. However, I did get some info. Firstly, lancer officers didn't wear 'greatcoats', they wore 'capes' (knuckle length) and 'cloaks' (ankle length and what we are talking about here). Description is:
LANCERS 385. Cloak and Cape - Blue cloth, of the same pattern as for Officers of Dragoon Guards and Dragoons, lined with scarlet, white lining in the 17th Lancers. In the 12th Lancers the collar of the cloak is scarlet, and in the 21st Lancers it is lined with French grey.
Lined with scarlet... that matches! So what pattern, you ask, were Officers of Dragoon Guards and Dragoons wearing?
DRAGOON GUARDS AND DRAGOONS 320. Cloak and Cape - Blue cloth, of the same pattern as for rank and file; to reach the ankles when worn on foot. White shalloon lining in the 2nd, 3rd and 6th Dragoon Guards and 1st and 6th Dragoons; scarlet in other regiments. Collar of cloak of white cloth in the 6th Dragoon Guards, red in the 1st Dragoons, black velvet in the 7th Dragoon Guards, and blue cloth in the ohter regiments. Red lining to the collar in the 1st Dragoon Guards and 2nd Dragoons. Buttons of regimental patterns. Shoulder straps of the same material as the garment; a small button at the top.
So without knowing exactly what the 'rank and file' were wearing I can't be sure. I did also look up the Royal Horse Artillery, who are also mounted officers of course. Their cloak is described as follows:
ROYAL HORSE ARTILLERY 425. Cloak - Blue cloth, with sleeves. Stand-and-fall collar with three black hooks and eyes in front, and three small flat silk buttons at the bottom to fasten the cape. Round loose cuffs, 6 inches deep. A pocket in each side seam outside, and one in the left breast inside. Four buttons down the front. A cloth back-strap, to fasten with a large flat silk button at the top of each pocket; a similar button in front on the right to hold the end of the back-strap when it is not buttoned across behind. White shalloon lining. The cloak to reach within 8 inches of the ground. Shoulder straps of the same material as the garment; a small button of regimental pattern at the top. A gusset behind as described in paragraph 14.
So again some features that match your cloak, in this case the same collar as on your example is described exactly, as are the sleeves and cuffs. In terms of raw info this is all I have for now. It's not proof positive, but does seem promising. I have never seen any Victorian coats to be honest with you. They are pretty rare I would think. By the way, the gusset described in para 14 is basically the big slit down the back side. Paragraph 14 is a general description of the officers' dismounted greatcoat, and the variation of it worn by mounted officers 'for whom it is authorized', hence the need for a gusset.