It looks like there's only one way that Amtrak will sell you a through ticket:
Cardinal from Chicago-Washington
Northeast Regional 66 from Washington to Boston (leaves Washington at 9:40 PM, gets into Boston at 8 the next morning.)
Thruway Bus (probably a Concord Coach) from Boston South Station to Portland.
The Lakeshore Limited gets into Boston 8 :10 PM -- if it's on time. I'm not sure when the last Concord Coach leaves South Station for Portland. Anyway, Amtrak won't sell you a ticket using that routing. You could do it if you want to stay overnight in Boston.
If you take the Capitol, you'll get into DC shortly after lunchtime, but I don't think they'll book you on a regional that leaves before 3 PM. A Regional takes about 7-8 hours to Boston from Washington. That means if you leave at 3 you'll get to Boston at 11PM to midnight. I'm not sure if there's a Boston-bound Acela you can connect to from the Capitol; that might save an hour on the travel time, but I suspect you'd still get into Boston too late to connect to anything going to Portland.
There is Amtrak train service that runs between Boston and Portland called the Downeaster. However it leaves from North Station, not South Station, which serves all the other Amtrak trains. (There are two train terminals in Boston.) The last Downeaster of the day leaves North Station at 10:30 PM and arrivies in Portland at 12:55 AM. If you took the Lake Shore Limited to Boston, you would probably need to use a taxi or Uber to take you over to North Station (It's only a 5-10 minute ride) to make the connection.(You could take the subway, but it involves changing subway trains and is a real pain if you have luggage.) But, of course, there's no guarantee that the Lakeshore Limited will arrive on time.
Personally, if I were doing the trip and I were taking the Lakeshore Limited directly to Boston, I'd just stay overnight in Boston, and go to Portland the next day. If I were watching my budget, I'd take Amtrak's routing via the Cardinal, Northeast Regional 66, and the Thruway bus and arrive in Portland at noon, as opposed to sweating a non-guaranteed connection in Boston and arriving at 1 in the morning.