First(ly), secondly, lastly. In such sequences where points or topics
are enumerated the choice of form as between first and firstly is
optional in modern English. (Fowler's Modern English Usage )
In practice many different patterns are used:
- First, ... second, ... third;
- Firstly, ... secondly, ...thirdly;
- First, ... next, . . . last; (AmE)
- First of all, ... second of all, ... thirdly;
- and numerous others.
Burchfield, in Fowler's, has hit it: "Logic did not and does not
come into it." Gowers, in the second edition of Fowler's (1965),
says "The preference for first over firstly in formal enumerations is
one of those harmless pedantries in which those who like oddities
because they are odd are free to indulge, provided that they abstain
from censuring those who do not share their liking.
Your "because-version" is grammatical, however, to me, it appears a little clumsy and wordy. I would keep the first "because".
First(ly), because it was my university's library, so I wouldn't have to walk very far. Second(ly), I liked the atmosphere. It was very modern. It had colorful furniture and shelves arranged as a concentric maze. Last(ly), it had the largest book collection in Taiwan....