Many railroads are so worried about people getting injured that they'll often offer people buyouts for early retirements. The last thing they want is someone getting hurt a year before they can retire and getting a settlement, so it's often cheaper for them to offer buyouts. My ex stepfather got a buyout from the UP, and he was working fucking clerical bullshit at the time. He was about as likely to get hurt on the job as an elephant is likely to fall out of the sky, and they still offered him a significant buyout to get him to essentially retire early.
Grabbit, you need to not fuck around with representation. I don't know if the attorney is decent or not, but if you don't either then you need to look elsewhere. You should know better than anyone how vicious the Railroads get about this kind of thing, and you also need to watch your back. If you don't settle then I wouldn't be surprised if you start having agents follow you around.
This shit is serious, and it isn't a slam dunk. I don't know if you were coming out of service or not when this happened, but with the way FELA is worded the RRs can try claiming that they weren't negligent, that the oil leaked during operation and that they had provided a "reasonably safe" work environment. They can go after you for shit as minor as not wearing approved boots, or even boots that aren't rated as slip proof or oil resistant, and you can end up with nothing. That's unlikely since most RRs have rigid boot programs, but that's just an example.
I don't know if the lying shit will be an issue or not, beyond possibly scaring you away from going to trial. The issue of your honesty, or lack thereof, means jack and shit when it comes to you slipping and falling the fuck off an engine. Especially when it's on tape. As far as who you choose, you want to go into it looking for someone that isn't afraid to tussle with the RR and someone who the RR might be more willing to come to terms with. This union dude, if you have a bad feeling then go fucking talk with this other guy. The first guy could just do the minimum the Union wants done so that they can claim that they're looking out for their local while simultaneously trying to avoid pissing the RR off and letting you get shafted in the process. In fact, I'd probably avoid anyone Union related for the simple fact that Union/Company politics are so in favor of the companies anymore that the risk might not even be worth it. I mean I don't know how the UTU is there, and I'm generally pro-Union, but I also have to say that the RR unions aren't but a pale shadow of what they used to be, many have no balls when it comes to standing up to the RRs and I've heard a ton of stories of local chairmen who gave zero fucks about the members and seemed to be more interested in using their position as a way to ingratiate themselves with RR management.
I'd change from the first guy for the simple fact that he wouldn't answer your question. That doesn't exactly inspire confidence.