No one listened to me?
It'd be impossible for Lucca to have gotten Doan in the same timeline that Crono and co. defeat Lavos; if she went into the future in the same timeline that Crono and co. defeat Lavos she'd end up in the prosperous future. However, she could've snuck away when the crew goes to 2400 AD, gotten Doan, and snuck him into the EoT...
Also, doing the smallest thing WOULD have an effect on the future... Ok, so I'll use the example of doing one thing or not doing it, which is basically the same as effecting the past. So I decide to move the chair sitting next to me over by a bit. The remote's sitting on the chair, and tomorrow I can't reach the remote since I moved the chair, so I decide not to turn on the T.V. Instead of watching T.V. I start listening to music on my computer instead, and because I didn't watch T.V. whatever television station notices one less person viewing whatever show. Instead of having 66,667 people watching whatever show 66,666 do. One of the producers, who's very religious, notices this as a sign and cancels the show. A new show gets put in its place and focuses on terrorism with a very pessimistic view, that America's about to be blown up. One of the president's cabinet member's wives sees the show and becomes insanely scared. Her husband soon also gets the same opinion, and influences the president to completely bomb every country with any history of any terrorism.
If I don't move the chair, I watch T.V., 66,667 viewers watch the show, the show continues, the cabinet member's wife doesn't watch the new show, her husband doesn't get paranoid, and the president doesn't bomb the Middle East.
Ok, so that's EXTREMELY coincidental, but that's in the course of a day. Over 400 years the difference can grow extremely big even without extreme coincidences.
However, my example is hypothetical because, as far as I'm concerned, I wouldn't be able to make the choice between moving or not moving the chair, because whatever happened to me before would determine which I would decide, like everything happens in a sort of cause-and-effect manner. However, I don't try to go against time-travel by claiming that there's fate, since there's no reason why time-travel can't be part of the effect of the cause-and-effect.