The River Limlight, the northern border of Rohan, was only about 100 miles from Lorien.
There surely must have been SOME occasional contact between Elves from Lorien and men from the Wold.
In addition, men (Beornings and others) still lived on the banks of the Anduin north of Lorien, down to maybe the Gladden Fields. Here again, they might have had some contact with Lorien and would most certainly have had contact with Elves from Mirkwood. I say that because there was certainly interaction between the Mirkwood Elves, the Dwarves of the Lonely Mountain and the Men of Esgaroth. In turn, these people (particularly Dwarves) travelled into Eriador via the High Pass that was guarded by the Beornings.
All these comings and goings must have led to some residual contacts at least with Gondor, not least by way of the Anduin and via Rohan.
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