I have never kept a lungfish,
That being said in my visting of many zoos and aquariums, I have only seen a few tanks were lungfish had tankmates, most are kept alone
The first one was a monster that looked like a log at Disney World, It was kept with Bichirs and OB Peacocks. this tank was several thousand gallons, but I saw a tank on youtube where a lungfish was kept with a big group of bichirs, an African arowana; I think a breeding group of African Cichlids may be a good idea too, just have a pile of rock they can retreat to and hopefully it wont eat too many.
The second is at the California Academy of Sciences, where Australian Lungfish are kept with a large shoal of rainbows. This idea is get a large group of nimble surface dwelling fish that should not be around the lungfish, from my experience of seeing them they mostly just sit on the bottom, I have seen them move, and they are pretty fast, an actual lungfish keeper might have a better clue on how fast one can move.
If I was getting a lungfish I would buy the local big box petstores out of Rainbows and Giant Danios, or start up a colony of ob peacocks or some rock dwellers from any of the lakes.
My guess on your question is it really depends on the lungfish, some may be peaceful, others might actively try and bite fish, and some will bite if presented the opportunity. Depending on how tall the tank is, arowana may be more safe, Probably Silvers are best because I have never seen a healthy/active one not just bellow the surface, while Jardini or African Arowana appear to be all over the water column, putting them in proximity to a lungfish. But people who have actually had lungfish are much more knowledgeable than me, I would like to hear about how active and quick lungfish are by someone who has observed them for a few years.