Gaia DR3 4975599907386148608 is a 11" companion sharing proper motion and parallax to lam02 Phe (Gaia DR3 4975599976104995328) and the pair is WDS J00357-4800 = KPP4421 in Washington Double Star Catalog. I suggest adding the following IDs:
for Gaia DR3 4975599976104995328 (lam02 Phe, HIP 2802), add: WDS J00357-4800A (new) ** KPP 4421A (new)
View object in Simbad 
for Gaia DR3 4975599976104995328 (lam02 Phe, HIP 2802), add:
WDS J00357-4800A (new)
** KPP 4421A (new)
for Gaia DR3 4975599907386148608, add:
WDS J00357-4800B (new)
** KPP 4421B (new)
Gaia DR2 4975599907385518720
TIC 616261349