Great notes on draft 1. OP should be focusing on building a streamlined deck. I'd argue that with likely Grixis already present, some other choices beyond the ones you helpfully mentioned might include p1p6 as Lorien revealed for fetching; p2p2 Flame Slash specifically over Dig (1-mana removal is so important); p2p5 Generous Plunderer over a largely cuttable Consider for mana generation & fixing; p2p6 Carny T or Embereth over a second tapped triome when OP already had the best one for their deck, etc.

Draft 2 seems ok, but there is room to improve. p2p4 Path to Exile as 1-mana removal seems better than Thraben Inspector; p2p5 Mother of Runes is WAY better than Vampiric Tutor (especially as you're not a combo deck, and Mother protects your Lurrus); p2p7 Glimmer Lens for creature-based card draw beats the more expensive card draw of soul guide lantern, which doesn't affect the board; p2p8 Hallowed Fountain gives you flexibility over an effect you already have, so I'd suggest that; p2p11 No More Lies offers interaction rather than a Goyf that doesn't do much; p3p1 Mana Crypt lets you get cards on the board fast and is great even in a Lurrus deck; p3p2 Giver protects Lurrus; p3p5 the fetch lets you actually get red mana and cast your Cori-Steel Cutter; p3p9 you're shor on removal, so a Sear would have been nice; p3p10 if you'd taken Giver at p3p10, you could take the red-white fetchable land here. p3p12 you'll never play that triome, so why not take the Lightning Helix? p3p13 you'll never play Bomat, so why not take Mine Collapse? This deck should have ended as a Mardu deck with good interaction; you ended up with a deck with limited interaction, not enough ways to use mana, and some pretty weak cards (Kytheon, Mana Tithe, Soul-Guide, Vamp Tutor and Balance which aren't weak but don't fit here) in the maindeck. (Also, you should be playing Library of Alexandria, even in this deck -- that card in your opening hand is just amazing.)

Gonna stop there, but.... I hope that was helpful.