Graphics have little to do with networking as they are rendered client side like in Eve. Graphics only impact your frame rate which is why a lot of capsuleers who often engage in massive fleet battles would tone down their graphics to maintain decent frames. However, it will not improve lag. Lag is something that is managed server side.

What time dilation does in Eve is slow down time to so that every command from every ship is processed in the exact order in which the server received them from the players rather than having the order get mixed up in haste. But this might not do well in a first-person shooter setting and lowering graphics will only help with frame rates but not with lag. You will still see rubber band effects and/or microwarping Legionaries on the ground especially when you have a massive fleet of over 2,000 capsuleers way above you over the planet you are on.

The fog of war for the moment seems to be a likely solution but other options need to be explored first before we can settle on that.

TiDi in Legion will have to be tested first to see if it's even practical. One way it would shown is that your character's vision will appear to altered to resemble a heightened sense of awareness with the surroundings appearing red as you hear your heart beating louder and louder and everything around you is slowing down. On the plus side this would seem awesome at first as you finally get a chance to quickly glance around as you're moving in one direction and being able to react more effectively if you catch someone emerging from a corner you wouldn't otherwise notice under normal time. The problem with this is that after a certain point, TiDi starts to make everything look like you're swimming through molasses. After that it will start to look boring and dull as everyone is just waiting a whole 5 minutes just for their character to run 10 meters. That won't be any fun at all especially if the maps are really vast spanning well over a couple of kilometers in size.

But it's likely that the connection between Eve and Legion will be through a series of battle servers rather than a direct connection with Tranquility. If that's the case, then the best course of action is to implement the following:

1. TiDi kicks in for both Eve and Legion in the affected constellation or node.
1a. If TiDi is above 75% of normal time, then both games will continue to experience TiDi for that given system, battler server, or node.
1b. If TiDi falls below 75% of normal time, Legion reverts back to normal time but all communications between Eve and Legion suffer a total blackout due to whatever interference is happening around you on the ground (throw in some lore to justify it) and also orbital bombardments are no longer accessible until TiDi is up to at least 75% of normal time. RDVs will also not be able to be called in due to the same interference as the Warbarge is probably experiencing similar blackouts in communications. TiDi in Eve will continue at the same time.
1c. If TiDi finally increases back up to 75%, then TiDi in Legion will kick in but you will be able to communicate, call in orbitals, and call in whatever your RDVs drop off.