You unlock Lazarus by having four Soul Hearts on your character at one time.
You can accomplish this a number of ways -
Keep an eye out for and destroying tinted rocks (identified with a 'x' on them)
Buy one for 5 cents in shops if they hold one
Curse Rooms sometimes have Red Chests with one or two Soul Hearts inside
Blue campfires can give Soul Hearts when destroyed with bombs
Angel Rooms can sometimes have two to three Soul Hearts inside them
Items that give Soul Hearts when picked up -
Squeezy - Gives 2 Soul Hearts
The Pact - Gives 2 Soul Hearts (Costs 2 Red Hearts in Devil Room)
The Mark - Gives 1 Soul Heart (Costs 1 Red Heart in Devil Room)
Black Lotus - Gives 1 Soul Heart (Secret Room Pool only)
Cancer (Zodiac) - Gives 3 Soul Hearts
The Soul - Gives 2 Soul Hearts (end game unlock so probably irrelevant)
Super Bandage - Gives 2 Soul Hearts
PJs - Gives 4 Soul Hearts (Afterbirth only)
Binky - Gives 1 Soul Heart (Afterbirth only)
Items that give Soul Hearts via effect
The Relic - Gives a Soul Heart once every 4 rooms
Book of Revelations - Active item gives 1 Soul Heart, takes six charges
Pandora's Box - Gives 2 Soul Hearts if used on Basement/Cellar/Burning Basement or 4 Soul Hearts if used on Depths/Necropolis/Dank Depths
Gimpy - Can drop 1 Soul Heart after taking damage
Dark Bum - Can give 1 Soul Heart after collecting 1.5 Red Heart consumables