Rights to intellectual property are not universally recognized. In those countries where they are, there are different agreements defining the extent of the rights.
In the U.S., a composer or songwriter automatically has rights to his or her creative work for a lifetime. In addition, those rights now carry on an additional 70 years after the death of the author under U.S. law.
The term of copyright for a particular work depends on several factors, including whether it has been published, and, if so, the date of first publication. As a general rule, for works created after January 1, 1978, copyright protection lasts for the life of the author plus an additional 70 years. For an anonymous work, a pseudonymous work, or a work made for hire, the copyright endures for a term of 95 years from the year of its first publication or a term of 120 years from the year of its creation, whichever expires first. For works first published prior to 1978, the term will vary depending on several factors.
So, to answer your question, there is no technical term I'm aware of that indicates "lifetime rights" since all rights under U.S. Copyright law extend for the life of the author and beyond. There are no 'five-year song rights", for example.
The entire business is quite complicated. There are publishing rights to a song as well. These can be bought and sold. They are separate from the copyright. When Michael Jackson purchased the rights to the Beatles catalogue he was purchasing the publishing rights only.