This did actually happen yesterday. Some poor sod with 1 Sanity got Lost In Time And Space and then, while still there, drew a card from the Dust Deck which made him lose 1 Sanity ...

Are there any rules for what happens in that situation? Does it result in a devouring? We just played that he got Lost In Time And Space all over again ...

There are no rules covering this as far as I know (other might know better) but I think you made the right choice. The AO simply decided to start kicking on the investigator already laying on the ground. They are really nasty buggers them GOO.

That's what I would've done, too.

an investigator LITS loses his turn, so I would rule that no dust card is drawn.

This came up in a game not too long ago. Amanda got stuck in LiTaS with Nightmarish Visions and 2 Sanity. This was compounded when the Endlessly Breeding rumour came up. That's the rumour you're not supposed to fail if the Black Goat is the herald, and he was. Amanda got hit every turn, and resent to LiTaS. Darrell, who had all of the money, got caught in the streets and went down under a string of hexes. I failed the rumour in short order, added 4-5 doom, Azathoth woke up, and we all died. It was close, as Jenny was in to seal the last gate. That's how all of my losses have been coming recently.

So yeah, I played it that way. Worked out okay.