Project phases like initiation, execution and closure are well defined. They have definite start dates, end dates, resource requirements etc. They also have a sequential relationship with one another. So project execution follows project initiation. Similarly project closure follows project execution and not vice versa.
Software development phases (requirement gathering, design, construction, testing, release) may or may not have this sequential relationship with each other depending on the software lifecycle methodology chosen. But definitely all of these software lifecycle phases fall within the time span which corresponds to project execution. So in a way project execution phase engulfs all of the software lifecycle phases.
Software development planning can be done during project initiation phase.
This way, software lifecycle and project lifecycle are linked to each other.