CAML_PersonID.xml

<Query>
      <Where>
           <Eq>
             <FieldRef Name="FieldName" LookupId="TRUE" />
             <Value Type="Integer">1</Value>
           </Eq>
      </Where>
</Query>

SPQuery_PersonID.cs

SPQuery query = new SPQuery
{
    Query = string.Format(@"<Where>
                                 <Eq>
                                   <FieldRef Name='{0}' LookupId='TRUE'  />
                                   <Value Type='Integer'>{1}</Value>
                                 </Eq>
                            </Where>", "FieldName", "1"),
    RowLimit = 10,
    ViewFields = string.Concat("<FieldRef Name='FieldName' />",
                               "<FieldRef Name='FieldName' />")
 
};