The problem is, that simply the appearance of a powerful enemy is generally not an incentive to leave for the players or the characters. For the players, you just dangled a nice juicy plot hook before them, something long-term like a powerful lich is a thing you can build a campaign around. For the characters they presumably have connected on some level to the starter area and the NPCs around, so leaving it behind when it is in danger would go against the heroic instincts of the usual adventurer. Boredom is the thing that sends people away, not the chance of death (because that comes with heroics, loot and adventure).
Use the hook
Your players will most likely want to do something about the lich, or at east they are liable to at least try. Give them the opportunity. The locals could send them to ask for help from the other continent. They could find information, that the lich's phylactery is on that other continent. If I understand correctly, they are small scale local heroes in the area, it is fully understandable, the people ask them to help out in a situation like this.
Grab them with another hook
Downsize the local threat (the lich), make the place peaceful and give the party some incentive to leave. Maybe the lich decided to go look for something, and locals asked the heroes to follow it. Maybe some wandering high-level adventurer party (future mentor/questgiver/ally/enemy) decided to step in, kill the lich and keep the peace around here. Maybe something else happened. Give them something to do elsewhere, preferably in multiple places. They are adventurers, somebody will find them with some job they can do. The important thing is to both give them an incentive to be elsewhere and make sure there isn't an incentive for them to stay in the starter area.
Burn it to the ground
This one may or may not fit with the tone of your campaign, and has a very good chance of setting up the lich as a long term goal for the party. Simply put, let the lich win. Have it bring the kind of overwhelming force only an undead wizard can use to decimate the continent and turn it into his fief. Have people run away from their homes, and let them start an exodus to continent two. Make it clear to the party, that they stand little to no chance on fighting back directly, but give them a chance to do something helpful, like defending the refugees and such.
The final solution
Just talk to your players. Tell them, you have some plans outside this continent, and/or give them an explicit warning about the danger. Outright telling stuff is klunky and inelegant method, but RPGs are a communal game, and sometimes a little talk can go a long way to smooth things out in the group.
Sometimes you have to provide some straight and powerful incentives for your players to move one way or the other. It is not railroading for the party to get offers they would be hard-pressed to refuse, if it is consistent with the world and comes as a result of their action. Make sure you have a reasonable explanation for things (or that you can think one up if it comes up in the future) and you are usually golden. Don't be afraid to make some changes to the pre-planned world, so the reality fits your explanation, because ultimately the whole thing exists for your and your players enjoyment.