This encounter is basically unwinnable for a Level 3 party.
A single Lich has a challenge rating of 21 which, according to this guide, makes it an appropriate encounter for a whole party at level 17. And we are talking just about one Lich, not three. Three at once would be an encounter no PC party would be expected to win, unless they are specifically min-maxed for such an encounter or get lots of help in form of DM fiat.
Why would your DM do thathave you face such superior enemies? Possible explanations could be:
- They are inexperienced and don't know what they are doing.
- They don't expect you to fight those liches. They expect you to flee or look for a way to get past them without fighting.
- They don't expect you to win the fight. They expect you to lose, and continue their story from there.
- Those liches are not actually the liches from the Monster Manual. Perhaps they are a homebrewed, much weaker version of Liches which your party can expect to beat on level 3. Or perhaps they are some other creature using some form of disguise (magic or mundane) to look like liches (so the old man is mistaken). Anyway, in neither case would we know what you are actually dealing with, so we can not provide much advise.
- The encounter is some kind of puzzle. There is some trick your DM expects you to pull off in order to beat those liches. Perhaps they expect you to use some unusual magic item you have or use something from the environment against the liches.
But I don't know your DM. So I can not read their mind.