I am not an expert but it looks like he may well be trying to court her- following her around, the chirping, head bobbing, and the moves toward her face (to try to touch beaks or regurgitate food) are all characteristic. Obviously Lucy is not particularly interested and is not shy about saying so.
Budgies do have a kind of puberty I guess, as they are starting to produce hormones and develop from a baby into a sexually mature adult. I've read this happening as young as 3-4 months but there's no set age for it to start. I don't think they really reach "breeding age" till about 1 year +, so that would be the puberty period I guess. Though I don't think adolescent budgies are any more sexual than adults, probably Rickey will always engage in these behaviors when he is in the mood for love.
Is Lucy the same age? She may just be not in the mood, or she may never return Rickey's advances. It varies with individuals just like with people...she won't necessarily pair-bond with him just because he's the only male available.
You should keep a general eye on them though. Budgie hens can typically look after themselves, but what you want to watch out for is either Lucy becoming receptive to Rickey's romancing (in which case you want to think about discouraging egg-laying unless you want and are ready to raise babies) or them becoming too aggressive toward each other and fighting.
Other than that though, just enjoy a chuckle at their antics!