No. You have to resolve things one at a time:
1. You play Lesson Learned, this triggers any ally abilities you might have, including Psionic Assault.
2. You first resolve Lesson Leaned. You select Psionic Assault from your discard pile and resolve its effect. You then take both Psionic Assault and Lesson Learned and banish them to the bottom of your deck.
3. You get to resolve any triggers you have waiting. One of them is the Psionic Assault ally ability.
4. Resolve Psionic Assault ally ability. It reads "Recall". Looking at the complete rules document, the keyword expands to "Return this card from your discard pile to your hand." You look for the card in your discard pile but the card switched zones so the game could not find it. You put the nothingness into your hand.
Also, while I was looking at the official wording for Recall, I found this sub-rule to recall:
5.4.2 Recall does not work unless the card is in the discard pile. Now, I am not Australian, but I think that that proves that I am right.