Yes, King Prasanajit who was Lord Rama's ancestor was also Lord Parashurama's maternal grandfather. So Lord Parashurama has links to Ikshavaku lineage.
From Chapter VII - Lineage of Puruvasas and Jahnu of Vishnu Purana,
Jamadagni married Reṇukā, the daughter of Reṇū, of the family of Ikṣvāku, and had by her the destroyer of the Kṣatriya race, Paraśurāma, who was a portion of Nārāyaṇa, the spiritual guide of the universe.
“JAMADAGNI (the son of Ricīka1) was a pious sage, who by the fervour of his devotions, whilst engaged in holy study, obtained entire possession of the Vedas. Having gone to king Prasenajit, he demanded in marriage his daughter Reṇukā, and the king gave her unto him.