I'm going to lviv ukraine in march. should I be worried about what's going on in the east? I'm from the us?

Lviv is close to the Polish border so I suspect the danger is minimal compared to the east part of Ukraine. Though I think the government advises to avoid non-essential travel to Ukraine.

You should be aware about what is going on in the East and keep updated by watching the news. But you will be safe in Lviv as it is miles away from the East. Ukraine is a huge country and it will take over a day by car, to travel from Lviv to the areas where the war is on going. So I wouldn't worry if I were you. I have travelled to Ukraine several times since the war started. I went to Kiev and Dnepropetrovsk which are much closer to the fighting than Lviv, yet it was peaceful in both cities. There are a lot of refugees in all cities in Ukraine as a result of the war in the east, so be vigilant and aware of your surroundings. You will also notice a lot of old people begging for money, which is very sad. I went during the winter and there were many elderly begging out in the freezing cold.

Yes, you should.

I would be.