Try this:
select distinct a.FirstName, a.LastName, v.District
from AddTbl a
inner join ValTbl v
on a.LastName = v.LastName
order by a.FirstName;
Or this (it does the same, but the syntax is different):
select distinct a.FirstName, a.LastName, v.District
from AddTbl a, ValTbl v
where a.LastName = v.LastName
order by a.FirstName;