Clean away the broken and cracked plaster on your wall with the putty knife. Slide the putty knife between the plaster and the wood framing and scrape off the damaged portions. The plaster will break off easily. Once you have cleaned away all the damaged plaster, apply shellac to the wood framing with a paintbrush. The lime in the mortar will eat away at the wood if you do not do so. Apply a thick, heavy coat. Allow the shellac to dry.
Fill a 100-ml beaker with sand. Fill the beaker with alcohol at 10-ml intervals. When the sand is completely saturated, total the number of milliliters of alcohol it required to saturate the sand. Divide that number by 10. That number represents sand in your lime-to-sand ratio. The lime number is always one. For example, if it required two 10-ml beakers to saturate your sand, your ratio is 1 part lime, 2 parts sand.
Alternate pouring sand and lime into the mixer at the ratio you determined. Allow the mortar to combine for 15 minutes. Do not add water unless the mortar crumbles and is flaky, and then, only at 8 ounces per 15 gallons of mortar. Keep the mortar away from heat and sunlight as you are mixing it. If you cannot avoid one or the other, add subtle amounts of water. Mix the mortar for at least 20 minutes.
Dump some mortar in your 5-gallon bucket. Allow the remaining mortar to continue mixing. With your trowel, apply the mortar to the damaged area. Dip your trowel in the bucket, scoop out a little mortar and fling it onto the wall. With with sweeping strokes, spread the mortar thin. If you plan to add a second or third coat, make sure your original coat is thinner than the undamaged area around which you are troweling your mortar. Allow your first coat to dry before adding a second.