Are lieder vocals generally non-gender specific?
As noted elsewhere, generally, yes. But some songs are sung "in character" as a woman or man who portrays or participates in some dramatic action. Different people have different tolerance for hearing a song that exclusively portrays (for example) a young woman's unrequited love for a man as she performs the (supposedly) womanly domestic task of spinning thread (Gretchen am Spinnrade, the text of which comes from an actual stage play).
Of course, a song recital is not a staged dramatic performance, so in fact it can work just fine for songs that portray a specific character to be sung by a voice that the character would never have. You're more likely to find the gender-specific attitude applied to entire song cycles rather than individual songs. For example, Wikipedia lists no recording by a male singer of Frauenliebe und Leben, and only one by a female singer of Winterreise. But in these days of cross-gender casting on the stage, it's fairly likely that a performer crossing these traditional gender lines would find a receptive audience.
There are also dramatic songs that portray multiple characters, both male and female. These songs have always been more readily accepted by singers of both genders (Erlkönig). And still other songs portray no character at all; these may be odes (Widmung, An die Musik) or stories told by a narrator rather than from the perspective of a character (Die Forelle, Heidenröslein). These too have traditionally been sung by singers of any gender.
I would imagine that other forms are specific to sopranos because of the vocal range generally required.
As noted elsewhere, it's quite common to transpose these songs. They've traditionally been published in volumes for high, medium, and low voice. These designations are used to avoid specifying the singer's gender: high voice may be used by either a tenor or a soprano, for example. Thus any song written for a soprano may be sung not only by a tenor but also by a mezzo soprano, contralto, countertenor, baritone, or bass.