Hi, I used to be at my wits end with lag on ps4, but lots of things can help make it better. My top advice is to give it time and let it load, I like to load my save not resume then hover over all the occupied lots in the world screen till the families pics load in then load my household and go and make a cup of tea while my sims do their own thing for a bit. I find if you give them things to do straight after loading they get stuck for a bit.
Going into Manage households and deleting a lot of currently not in world other household families really helps too, so does getting rid of everything in household fridges, inventory etc before moving on and starting a new save.
Or you can be really brave and delete any saves you haven't played in ages. I had a full ten saves originally and now I have three and that has greatly improved my lagging.
Hope some of this helps you too.