The first time I made the LSL->EB connection (2:15 departure), we were late enough that we all had to walk directly from the LSL to the EB, which left as soon as all the LSL passengers boarded. I don't remember if they held it for us and it departed late, or if we arrived minutes before 2:15. I think if we had been a little later, they would have held it for us. As I recall, there were about 20-30 passengers making the connection. So it is certainly possible for the LSL to be late enough to miss the 1:45 TE, but that was the only time it was close and I've never actually missed the connection.
Usually (i.e. every other time I've tried), there have been hours to spare, including connecting to the EB and TE several times. Other people on this site have ridden many more times than I have, but I wouldn't worry about it.
If you absolutely have to reach San Antonio that day. If so, I might consider arriving in San Antonio the day before. I think Amtrak will pay for your hotel in Chicago if you book the connection on a single ticket and the LSL is late. If your destination is actually on the Sunset Limiter west of San Antonio, it doesn't run every day. I don't know what happens if you miss your connection then.