A common question is whether Marx trains will work with Lionel crossovers, or vice versa. The answer is not well, but with a caveat. A big caveat. Here’s what to look out for with Lionel crossovers and Marx trains.
Marx only made a 90-degree crossover, also sometimes called a figure 8 crossover. The design of its early metal crossover isn’t forgiving of the pickup rollers on many Lionel trains. I would expect the rollers to get hung up on the middle of the crossing, and eventually damage the rollers. Don’t use these Marx crossovers with other brands of trains unless all of your other-branded trains have sliding shoes like Marx trains do.
Some of the later Marx crossovers look like they would be more forgiving to a Lionel locomotive, but I don’t have any experience with them. If you want to try one with a Lionel, try rolling the Lionel over it by hand first, before setting it up and applying power. If you feel the rollers hanging up on it, don’t use it. Used Lionel O27 crossings are inexpensive, so it’s not worth damaging your locomotive.
Lionel made 45- and 90-degree crossings, and later Marx trains with double-reduction motors work perfectly with them. Marx trains with the older, simpler single-reduction motor and the gear that extends all the way to the edge of the wheel have a bit of difficulty on Lionel crossings, however. They work, but they tend to bounce a bit, so you can expect the occasional derailment. An 0-4-0 locomotive will fare better than a 2-4-2 will, since it has half the number of wheels that can derail. It will also be easier to put back on the track as well if needed.
That said, Lionel trains are more prone to derail on crossings than on switches or regular track too. And their more complex wheel arrangements make them harder to put back on the track, especially for kids.
Ultimately you have to decide if the occasional derailment is worth it. The crossings definitely make layouts more interesting, so you may decide it’s worth the trouble. My recommendation is to try it out on the floor first. Then, if it works, mount the track on a layout.
What about mixing other types of track? Generally that tends to go better.