Chisel out the weak mortar in the joints between the brick and cement steps. As soon as you reach solid mortar, stop chiseling. Removing an even 1 inch layer of mortar is often all that is necessary to reach solid material.
Remove the chiseled mortar chips with a wire brush.
Fill a wheelbarrow with 10 parts sand, 5 parts lime and 1 part cement.
Stir together the lime, sand and cement with a garden hoe or shovel to fully integrate them.
Pour small amounts of water into the dry lime, sand and cement while stirring with a shovel until the mixture obtains the consistency of peanut butter.
Dampen the old joints with water. This will help the new mortar adhere better.
Scoop the mortar out of the wheelbarrow with a trowel and pack it into the joints in an even 1/4-inch layer. Allow this layer of mortar to dry for 15 minutes before adding the next 1/4-inch layer of mortar. Repeat this process until the mortar is level with the surface.