You do not actually want an array type, but a string representation. Can be achieved like this:
CREATE OR REPLACE FUNCTION "alarmEventList"(sampleid integer
, starttime timestamp
, stoptime timestamp
, OUT result text) AS
$func$
BEGIN
SELECT INTO result string_agg(concat_ws(','
,to_char("Timestamp", 'YYYY-MM-DD HH24:MI:SS')
,"AlertLevel"
,"Timestamp" - ts_lag)
, ' | ')
FROM (
SELECT "Timestamp"
,"AlertLevel"
,lag("Timestamp") OVER (ORDER BY "Timestamp") AS ts_lag
FROM "Judgements"
WHERE "SampleID" = sampleid
AND "Timestamp" >= starttime
AND "Timestamp" <= stoptime
) res
WHERE "AlertLevel" > 0;
END
$func$ LANGUAGE plpgsql
The manual on string_agg() and concat_ws()
.