My unreserved apologies. I’m seeing theism when it isn’t there. But… 
we are talking origins…
There is no doubt in my mind that the pre-LUCA, i.e. pre-genetic code “with ‘high fidelity replication’ and ‘and at least some rudimentary early form of molecular proofreading’”, Ur-organisms of late biogenesis engaged in gene transfer, just as all organisms do today. As per the hypotheses link.
My comment “Once we had Theobald’s (2010) and Saey’s (2010) LUCA there was no possibility of gene transfer from any other LUCAs” is based on the feeling that gene transfer from other LUCAs that all died out in the late Hadean-Eoarchean would have been prevented as as each LUCA will have had a different set of amino acids? Assuming different triplet coding bases? Which seeing that all four have been found found in meteorites would indicate not… so what other mechanisms would have blocked gene transfer from other LUCAs which died out? Perhaps none, but our LUCA dominated, out-competed them to extinction. How?
What would have differentiated competing LUCAs engaging in gene transfer? Or with sufficient gene transfer did they all homogenize to a single dominant LUCA with no more possible gene transfer from lesser LUCAs?
All the evidence is for LUCA. That is agreed. By science. Therefore how can there be any disagreement here?