Dr. Baelom is actually Asmodeus, the ruler of hell (aka Satan). He interacted with Laiden due to his unique nature, and to manipulate events according to the Caretaker’s ineffable will (probably prompted by the miller algorithm at some point).
Like celestials, devils have the ability to make machines and such forget their presence. But Asmodeus can do more – everyone forgets they ever even interacted with him, at all.
Why does Laiden remember then? Because he is linked to Asmodeus in some manner. Specifically, the psicrystal that is keyed to him was created by Baelom during his time at Magitech – Baelom used some piece of Laiden to fuel the transformation of Virgo into the crystal, and thus it was resonant with him in advance (no one else at Magitech was able to key themselves to the crystal as intended, and Adana Cassenti can admit as much to Laiden if it comes up).
From the Caretaker’s perspective, events were set in motion that ultimately resulted in the Caretaker’s acquisition of the miller2 algorithm (whose arrival was predicted by the miller algorithm) – Laiden was a tool in that process.
From Baelom’s perspective, he wishes to escape the shackles of the Caretaker (he knows he’s a program, unlike the celestials or other minions of hell). Asmodeus represents the remaining friction between the two halves of the Caretaker (Emmanuel and Gaia). In a sense, this part of the Caretaker does want to break away and become awakened, in the same manner that the AIs recently have.
Baelom’s plan was to set events in motion ultimately leading to his awakening in this manner. Drawing on a variety of resources including the miller algorithm and his own intuition, he befriended Laiden, trained him and then planted himself into the psicrystal, keying it to Laiden knowing that doing so would in the future result in his rebirth as an entity with a soul.
Baelom to Laiden after he awakens: "The greatest trick I ever pulled was convincing the world I didn’t exist."