Posted: 12/8/15 at 5:59pm
Assuming you consider the following paraphrases to be acceptable:
Gay - biological male who identifies authentically as male, not female, and is sexually/romantically attracted to men who generally identify as male themselves.
Transgender female - an individual born biologically male who identifies wholly as female and is attracted to men, both sexually and romantically, are authentically men
*I know - the problem: "Who says what a man is? What makes a man? Girls can play football, too." I'm going with the common sense, million-years-old hunter/gatherer framing device - the one we each use everyday of our lives.
Since the musical never really goes into Lola's sexual or romantic life, I know I cannot say to whom she is attracted (in either capacity); however, I fell like I can say with confidence that Lola identifies as female (she does not just perform as female - she goes to the factory that way, as well). It's just not possible (as several others have noted) to pin down a clinical definition of her in this regard. If you subscribe to the usually-true walks-like-a-talks-like-a ideology, I think you'd have to venture that she is a transgender female. As Terrance...Mann notes, I like that it's never addressed.
I also agree it's odd that (I believe) at some point Lola references/implies/allows the inference that she is straight - it's easy to jump the gun and think, Oh - a straight male. Lola says that, I believe, because (instead of the Frankenstenian term "transgender female"
she identifies as a straight female.