If something happens adventitiously, it happens by chance, not because someone arranged it. It is simply adventitious with -ly, so it keeps the same formal, slightly scientific feel. You will almost never hear it in conversation; it belongs to careful writing and to science. In biology it can mean in an unusual place, not only by luck: a root may grow adventitiously from a stem. Do not use it as a fancy synonym for luckily. Luckily is warm and everyday; adventitiously is cool and exact — it only says the thing was not planned.