Upgrades Options by AA operated flight but BA marketed and stock
 

My company booked me on BA but because the ticket was purchased via BA, I can't upgrade nor am I able to use my miles nor status to upgrade to PE or Business Class. When I check in, if seats are available, will I be given the option to purchase an upgrade to PE or Business?

You may be offered an LBFU if there is a lot of space. But unfortunately , as it is BA marketed there is no way to use miles/copay or SWUs.

Is it a BA codeshare on an AA flight ot is it just an AA flight booked via BA?

BA*AA flights (Y and B booking classes only) can be upgraded with AA miles. The issue here is that the ticket was issued on 125 (BA) stock. Some members here claim that AA does not care about the ticket stock but it seems that AA does.

Ticketed via BA on an AA operated flight.

Not who issued the ticket but what is the flight number? is it a BAxxxx flight number or an AAxxx number

-that- is the reason you were not able to upgrade, -not- the reason you were replying to (AA-issued ticket vs. BA-issued ticket on a AA operated/AA #'d segment.)

Did you meet the other condition (being booked in Y or B booking classes if it is a BA-coded flight)?

Here is the flight information from the ticket:

Flight BRITISH AIRWAYS BAXXXX (AMERICAN AIRLINES)
DEPARTURE London Heathrow (LHR - Terminal 3) ARRIVAL Dallas/Fort Worth Intl (DFW - Terminal D)
Booking status Confirmed Flight duration 10:15 (non-stop)
Equipment Boeing 777-300er Passenger Meal available Lunch
Class Economy/Coach (B)

The booking class is eligible for an upgrade to Premium Economy ( if there is award availability) however , as per https://www.aa.com/i18n/aadvantage-p...r-airlines.jsp

Reservations booked through a source other than American Airlines must include at least one flight with an American Airlines flight number in order to be eligible (includes codeshare flights operated by British Airways or Iberia but booked as an American Airlines flight number.)

Do you have any flight in your itinerary that is booked as an AA flight number? If so, then you meet the eligibility requirements , otherwise you will have to settle for travel in economy ( or pay fare difference )

No, just BA.

Look like my only option will be to get a LBFU on check in. Will I be able to check in on AA.com for the AA operated flight from LHR-DFW?

You will, I believe, check in on the BA website - I would not expect to get any discounted offer at check in for an AA operated flight

You would have a better chance if you were to switch to a BA flight