AA EXP DFW-LON,
Unfortunately I can't answer your question, because I haven't been on a LX flight in a while, but considering that the first leg of your trip is on BA out of LHR, I'd be more worried about BA.
BA's carry-on limit in Y is a ridiculously low 6 kg

while LX has a more reasonable 10 kg limit. Based on my (admittedly limited) experience and on what I've read here on FT, BA is pretty strict on carry-on weight limits, especially out of LHR.
You may want to do a search in the BA forum regarding this topic.
andy