I didn’t think onboard streamer and DAC were on par with the quality of the pre/amp when I had the H390. I think the streamer is on a level with some costing a few hundred bucks, like the Allo USBridge Sig I had, and the DAC maybe $1k-ish. Using a dCS Network Bridge and MHDT Orchid DAC (upgraded) brought a lot of refinement, depth, and musicality over the onboard DAC and streamer, which were a bit sterile with flat imaging by comparison. This held true for each component independently, using DAC loop to pair the onboard streamer with the Orchid, and Network Bridge feeding the onboard DAC over S/PDIF.
While I haven’t heard a Lumin T2, I had an X1 and it was pretty extraordinary. Many great things have been said about the T2 as well. I would bet that you’d be very happy going from the built-in digital of the H390 to the T2.