In general they work, but as other have pointed out there are some slight issues with some lenses:
1) The Panasonic Lumix 7-14 f4 produces purple ghosts on Oly bodies. The cause is a lack of UV filtering which then gets reflected between sensor and rear lens element causing ghosts. The problem depends on the light source and its position in the frame so it's not something that you'll necessarily experience, but when it happens it can be impossible to remove in PP. Examples aplenty here::
https://www.dpreview.com/forums/post/50723994
2) The AF motor in the Panasonic Lumix 20mm f1.7 can cause electronic interference at high ISO leading to banding effects.
3) The position of the screws holding the mount to the camera are further away from the centre on Oly cameras than Panasonic cameras. As a result, the weather-sealing ring on some Panasonic lenses sits on top of the screws meaning that the seal is not effective.
4) There are reports of mount binding on some Panasonic lenses on Olympus cameras - the PL 100-400 seems the most prevalent.
5) Lens IS does not work in concert with IBIS across brands - so Oly camera/Oly lens works, as does Pany camera/lens, but not any hybrid.
However, the list is probably over-stating the problem. I've used Panasonic lenses quite a bit over the years with Oly cameras (12-35, 35-100, 7-14, 20, 15, 8-18) and none of the above was a deal breaker. I've let most of them go, but still have the PL8-18 which is a great lens and works on my EM1.3 with no issues at all.