its hard to say from pic what type of plastic that is. there are some types, nylon, polyethelene/propylene based plastics that cant be easily glued back together, some not gluable at all with glues and adhesives you will be able to buy. if you have a tube of superglue. put a drop on the plastic, let it dry and try to pry it off. if it pops off your lid is most likely one of these plastics and trying to glue it will be useless. in that case mechanical fix is needed.
i would recomend a mechanical fix/brace even if it is gluable. that looks like a cross brace on top of tank which has a ton of stress from water in tank. i personally wouldn't trust any glue to hold that kind of stress. i worked for a company that manufactured epoxy adhesives for years and we also made acrylic aquariums in our fabrication shop. if it was my tank i would get new lid or mechanical brace.