Lace\Pearl Gourami's

The aggression: it is normal for male gouramis to chase female gouramis. Some species have a worse reputation than others (all varieties of 3-spot and dwarfs) but that doesn't mean the less aggressive species don't do it. In a lot of fish, including gouramis, the male chasing the female stimulates egg production in the female. One possibly answer is to get another female, if you can find a shop that'll sell you a single one as most seem to sell pairs. With your tank being 180 litres there should be enough room. You would need to keep an eye out that the pair would accept the newcomer. I had a pair of honey gouramis, I got a second female and the new fish bullied both of the pair! You just never know with fish.
Is the male displaying to the female at all? I've never had pearls but I've had honeys for years. With them at the beginning of 'courtship', the male displays to the female and if she doesn't respond, he chases her. The female often ends up with a nipped tail, but it heals quickly. After a while the female will start to respond leading up to spawning after a few days. Are your pair doing anything like this? Any sign of a bubble nest?

The fat female: yes, female gouramis are usually fatter than males when mature. It's one way to tell the sexes apart in species where both look the same colour. Maybe the male's chasing is stimulating egg production. Just make sure she is plump not ill. All gouramis are prone to bacterial infections, some like dwarfs are just much more prone. Make sure her scales are lying flat and the fatness is the same on both sides. If it's just on one side, that is not a good sign.

Assuming that's the male in front, he has a lovely orange throat. If they are anything like honeys, the throat colour gets more intense when he is 'in the mood'.