There are mentions of a few Composite Forms = half masculine & half feminine depiction = of Sriman LakshmiNarayan bhagvaan ji in the core vaishanava scriptures like the Pancharatas scriptures.
For example = the Shri Paadma Samhita describes the murti (icon or idol) of one such composite form known as Abhinna LakshmiNarayan.
It is found in Paadma Samhita -> KriyaaPaad Adhyay - > Chapter 18
Verse 52 - Verse 53 =
अभिन्नालक्ष्मिनारायणमूर्तिः
वपुषो दक्षिणे भागे विष्णुर्वामे सरोरुहा
पीनस्तनतटो वामश्श्री वत्साङ्कस्तथेतरः
वामो हेमनिभश्श्यामो दक्षिणो भाग इष्यते
आसीनं वा शयानं वा गरुडारूढमेव वा
On the right side of the body of the icon of the Abhinna LakshmiNarayan Murti, there is Vishnu, and on the left, there is Lakshmi (Saroruhaa). The right side symbolic of Vishnu's chest is marked with the Srivatsa symbol, and the left side of the icon is representative of Lakshmi's vaksha-sthala . The icon is dark complexioned on its right side (Vishnu's complexion) and the left side is golden complexion (Lakshmi's complexion). The icon may be depicted as either seated, or lying down, or mounted on the Garuda.
References for the Paadma pancharatra Samhita is = https://archive.org/details/PadmaSamhitaSeethaPadmanabhanSampathR.N.Vol1/Padma%20Samhita%20%20Seetha%20Padmanabhan%20Sampath%20R.N.%20Vol%201/page/n171/mode/1up