Makefile - no such file or directory error

There are a number of issues with your Makefile (beyond the question of whether a Makefile is the appropriate solution):

• conditional directives aren’t part of a recipe, so they mustn’t start with a tab;
• conditional directives are evaluated as the Makefile is read, so variables must be assigned previously and can’t be target-specific;
• docker ps -a returns information on all known containers, including non-running containers;
• phony targets should be declared as such.

The following works:

result = $(shell docker ps -f name=myapp -q | wc -l)
start_docker_myapp:
ifeq ($(strip $(result)),1)
    @echo true
else
    @echo false
endif

.PHONY: start_docker_myapp