Can ovulation happen 27 days after lmp - a day or two before your next expected period?

No: It could happen 27 days after your period, but then you would not have another period until 2weeks later. You would not be able to have a period 1 day after ovualting (it would be 2 weeks after ovulating).

Yes, though rare: The luteal phase, the time from ovulation to the next period is usually at least a week, and up to two weeks in length. Late ovulation indicates a problem, either with egg quality or the pituitary ovulation signaling mechanism. Bleeding out of normal cycles should be evaluated by a gynecologist or fertility specialist. Testing with ultrasound and blood test is helpful.

No: Probably not. Ovulation occurs 14 days prior to your next period with regular cycles.