Postgresql update json data property

Use the jsonb concatenation operator (Postgres 9.5+):

update log
set result = result::jsonb || '{"lat":"123"}'
where id = 6848202

In Postgres 9.4 use json_each() and json_object_agg() (because jsonb_object_agg() does not exists in 9.4).

update log
set result = (
    select json_object_agg(key, case key when 'lat' then '123' else value end)
    from json_each(result)
    )
where id = 6848202

Both solutions assume that the json column is not null. If it does not contain the lat key, the first query will create it but the second will not.

In PostgreSQL 13, You can:

update public.log set result = jsonb_set(result,'{lat}','"123"') where id=6848202;