I have never come across a pair quite the same as these so it is hard to state the provenance and online searches have been of no help so I will provide lots of photos and describe them to the best of my ability. I believe they likely have some good age as they have come from the home of an avid collector of Asian artefacts, unfortunately the items were not catalogued or labelled.
Pair Of Primitive Antique Pottery guardian lions often referred to as Foo Dogs. I think they are a terracotta clay rather than carved sandstone.
They are each approximately 9cm long x 5cm wide x 10cm tall.
They are incense burners with a space for an incense cone and little holes for smoke to escape or maybe to hold incense sticks.
They look architectural to me, perhaps some kind of tiles?
They are certainly very primitive in appearance although I hesitate to call them ancient, I think more likely Qing dynasty (19th century) however this is just an educated guess.
The condition is evident in the photos I’ve provided, they are weathered and worn with chips and little flaws, one of them has significant surface wear on one side where whatever was used to seal them (glaze or paint) has eroded. I wonder if they have spent substantial time in water or buried in earth although the condition could also be consistent with being something from the outside of a building such as a tile as suggested above.
There is evidence of a dark residue on the base and some greyish, white marks on the statues that can be seen in the pictures, they appear quite clean, I have only given them a gentle brush and I will not attempt to clean them any further as will leave to someone who knows what they are doing.
Please look closely at all photos for a clear and honest description.