The main problem posed in this question concerns tenses. You need to realize the sequence in which the events took place.

1. the Philological Society launched its effort to create a dictionary - 1860 so PAST SIMPLE

2. now we need to decide what tense should be used to talk about the duration of the project - it started in 1860 and continued for 60 more years - therefore we need a structure which will show the duration from the point in time (1860) into the future (60 more years). However, that period has already finished (in 1920). Which structure can demonstrate that?

3. now the last problem - when was the dictionary born? before the project was launched or at the same time? is being born rather a short action or a longer background action?