Presumably you mean the Bill and Hillary Clinton National Airport, LIT. There are NO OW flights YVR-LIT connecting through DFW and MIA. There is also no codeshare availability YVR-DFW-LIT on that day.

However, there is D availability on codeshares YVR-DFW and, separately, on DFW-LIT on July 21. So what you really have is a married segment problem. You're going to need to talk to a human at AA.

Now, if you actually meant LIR, then you have a different problem. Sort of. There's codeshare space available YVR-DFW and DFW-MIA. Your real problem is the MIA-LIR segment. AA runs two flights daily except Tuesday, when the afternoon flight doesn't run. There's plenty of D space open, but no codeshares. Again, I think that your best bet is to call AA and speak to a human. You're looking for a three flight routing which has codeshare space on ⅔ of the itinerary and plenty of D space overall. Perhaps you can get someone at AA to free up the space you need....