Lyrical dance is a literal representation of music using a combination of ballet and jazz with a little bit of modern thrown in for good measure. It is usually performed in foot undies and tends to be romantic and emotional in approach. The speed of the dance, whether upbeat, or slow and more balletic makes no difference. There is no "lyrical technique". You use your ballet (or Jazz, depending on the direction the teacher/choreographer takes) technique to dance emotionally to the lyrics of a song.
Lyrical, modern and contemporary are NOT all the same. The problem is most people (including many dance teachers and owners) don't know the difference and explain the genres by incorrect names or just tend to lump everything together. They even make up names for non existent dance genres that are specific only to their own school. That is why many will answer "contemporary" or a mish-mosh of answers because that is what their school calls it. That doesn't make their answer correct.
Modern dance is a specific discipline. There is Graham, Horton and Limon to name the top 3 styles. There is also Dunham and Cunningham. Later styles like Alvin Ailey came out of Horton and Paul Taylor out of Graham. They are danced barefoot and are grounded as opposed to the floating one usually wants in ballet. They are all based in rules for their specific style of modern.
Contemporary dance has no technique of it's own and relies on both Ballet and codified modern technique. It is the choreography that makes a dance contemporary. Contemporary dance can be done en pointe, barefoot, in socks or anything else the choreographer can come up with. Often contemporary is abstract and devoid of any emotion at all but just simple line and movement. Any type of music, noise, the spoken word, or even no music or sound at all can be used.
As things considered, the Lyrical dance form would be an enjoyable, creative and self-expressive way for students to explore movement, especially when taken in tandem with traditional ballet lessons.