According to this timeline, Prince Tommen Baratheon was born in 291. Later in year 293:
Jorah Mormont is caught selling poachers and flees from Westeros to avoid execution by Lord Eddard Stark.
As you can see in the map below, if Jorah set out from Bear Island to sail to Essos, he would have had to sail around the western shores of Westeros and past Lannisport:
Eddard sailed to Bear Island to find Jorah, as he recalled in Chapter 12 of AGOT:
Ned had made the long journey to Bear Island, only to find that when he arrived Jorah had taken ship beyond the reach of Ice and the king's justice.
It is possible that Eddard might have continued sailing - or planned a longer voyage - to see if he could still catch Jorah anyway.
Lannisport is one of the major ports of the Seven Kingdoms and is the largest settlement in the westerlands. So it is an obvious place of interest if you are on the trail of someone fleeing by ship. Coincidentally it is also where Jorah met his wife and where Cersei could have been at the time (perhaps as an opportunity to get away from Robert for awhile, as others noted).
There is no evidence for any of this, unfortunately, but we do know Eddard is man willing to take matters into his own hands - "The man who passes the sentence should swing the sword."