There are plenty of Lifestone shards and cores to be found in the game. Below is a list of all of them and the levels they can be found on.

Vulgrim (soldier artifact reward): 1 shard and 0 cores
Vulgrim (champion artifact reward): 1 shard and 0 cores
Serpent Holes: 1 shard and 0 cores
Crossroads: 1 shard and 0 cores
Scalding Gallow: No shards or cores
Choking Grounds: 2 shards and 0 cores
Broken Stair: 2 shards and 0 cores
Twilight Cathedral: 1 shard and 1 core
Drowned Pass: 2 shards and 0 cores
Anvil's Ford: No shards or cores.
The Hollows:1 shard 1 core
Dry Road: 1 shard and 0 cores
The Ashlands: 2 shards and 1 core
Iron Canopy: No shards but 1 core
The Black Throne: 1 shard and 1 core
Eden: No shards or cores

This will give you a total of 16 shards (equal to 4 cores) and 5 cores.