In support of (2), if Rand could access the Moridin's Mindtraps via their connection, it follows that this could lead to dream invasion by Rand to Lanfear. However, I view this less likely than (1) because (1) already has an established precedent.
In either case, the question then becomes whether this occurred by mere happenstance, or whether Moridin manipulated events. I personally think this was a totally random and unpredictable event, probably due to their mutual hatred given the precedent introduced by Egwene/Gawyn in Book 6.
Despite Lanfear's hatred of Rand, I have to believe she would do anything at this point to get out of the mindtrap. She's already expressed a desire to betray the Dark One with Rand using the CK in earlier books, and that was when she had a high position among the Shadow. Now that she's a virtual slave, she'd only have more incentive to do so. As mentioned before, she could very well have critical knowledge regarding the Bore --- knowledge that LTT never had, unless Beidomon survived and was questioned after the Bore was made.
In conclusion, I think this was for real and was not a trap. Lanfear was never particularly loyal to the Dark One, and now has every reason to ditch him altogether. If Rand can break her free of the Mindtrap he may very well have an ally that can provide him with mission-critical information for sealing the Bore. Of course, since at the end of ToM he plans on going to Shayol Ghul the very next day, could this possibly be accomplished in time?... I don't know.
I think there are lots of links. We know that Nynaeve can sense Egwene thanks to healing, so they have a kind of bond, Lanfear probably has the same bond with LT. Lanfear is a skilled dreamer and can probably use "need". Moridin is linked in dreams to Rand thanks to balefire. The Finns might have done some things to them.
I think Cydane is broken enough that she will turn on TDO when Rand frees her, in fact I wouldnt be surprised if Cydane and widow Nynaeve ends up helping Rand with Callandor all dying in the process.