Been mulling a theory. He approaches the bench, befriends a peed off, upset and freezing young lady. Offers her a lift/sit in car/help getting into house. He opens the car, helps her with a blanket, which explains the slight pause/shuffle before she gets in. Drives down Beresford , bypasses her house, parks up, exposes himself. LS runs out of car into park and after a time of running finds the bench to sit onto catch her breath, to wait to see if the coast is clear. Is spotted by someone, gets spooked and runs off again.
To me, the time line of him being seen driving down Beresford and almost straight away back up Wellesley onto the main road fits.
Whether he then returns to the park or LS becomes disorientated and loses her footing is anyone's guess. Feel free.