The “executive summary” is “not a problem”. But, let’s go into details.
The lake itself is a very old volcano crater and there are three volcanos surrounding it. But, there is little reason for concern. While there are active volcanos in Guatemala, there is nothing active around the lake and there has not been for thousands of years. The photo is of Santa Maria which I took from out B&B a week ago. It is closer to Xena (Quetzaltenanco) than here and on the other side of the volcanos and mountains which ring the caldera.
Another good question but not an issue. Sure, you will feel earthquakes here sometimes but there are places where they generally occur and they are not close.
One such area is near or off the Pacific coast. They are typically of a magnitude between 4 and 5. If you are not doing anything active you will probably feel them but I know of no property damage near the lake.
The others occur northwest of here. Again, on or near the coast at the Guatemala/Mexico border. There has been some property damage in that area from the quakes but, once again, nothing near here.