You can, but it's probably a bad idea. You won't be able to use an entity retrieved from one context with the other (not directly anyway). To write to an entity retrieved using the "read" context you'll have to read it again using the "write" context in order to modify it.
Instead, you can simply enable or disable lazy loading as needed before you make use of your context.
DbContext.Configuration.LazyLoadingEnabled = false; //or true
You could make it easier by simply defining a custom constructor for setting the LazyLoading attribute.
public MyDbContext(bool LazyLoad)
: base(nameOrConnectionString: "MyDbContext") {
this.Configuration.LazyLoadingEnabled = LazyLoad;
}
If you really really need to, you could subclass your DbContext and set LazyLoading in the constructor, but it just seems like a bad idea.