There's no need for loops or inner selects. Just try this:
UPDATE table1 SET column1 = column1 + column2
It's allowed to read from columns in the set clause:
set
UPDATE table1 SET column1 = column1 + column2WHERE rowid = 1
For all the rows you need not WHERE predicate:
WHERE
UPDATE table SET column1 = column1+column2
thats all.