A lovebird and budgie mating?

start off have (female) budgie approximately 4 years old.
(male) lovebird 3 , half years old based on store told me.
each have separate cage themselves.

time now, female has laid infertile eggs throw out.
lately, noticed left me curious.
whenever let lovebird out business atop cage covered towel, raises tail @ 90 degrees angle; made me wonder if lay eggs or if feeling rather "hormonal."
opened cage door , watched lovebird crept in.
began feed regurgitating seeds. @ bottom perch , in 1 moment, lovebird hopped on top of , "did business."

question possible have lovebird , budgie hybrid?

have read somewhere on forums same thing occurred , egg hatched bigger budgie.
however, couldn't entirely sure since owner hasn't checked on daily basis.

question might seem bit silly, know.

to start off have (female) budgie approximately 4 years old. (male) lovebird 3 , half years old based on store told me. each have separate cage themselves. time now, female has laid infertile eggs throw out. lately, noticed left...

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