Tapeta lucida have evolved a ton of times, and they’re probably not ancestral to birds. They’re typically associated with nocturnal birds – kiwis, kakapos, owls, and nightjars all have them, and they’re all over the bird family tree.
So the way to answer this question might be to first answer the question – were dromaeosaurs nocturnal? And this is one we may be able to answer. Unlike humans, dinosaurs have bones in their eye – yes, in their eye – called the sclerotic ring. (As their eyeballs are not spherical but more of squished spheres, these bones help the eye keep its shape instead of popping out into a sphere)
Nocturnal animals tend to have bigger eyes. This makes sense – a bigger eye means more light can get in, and when you’re always out at night you want to be able to see what you’re doing. By looking at sclerotic rings, some teams of researchers have concluded that Velociraptor was likely nocturnal. Are their methods sound? ….Maybe. One issue with sclerotic rings is that they’re not one bone – they’re made up of a ton of individual bones called sclera.
This means that after death, as the carcass is rotting, the sclera can become disarticulated. It can be difficult to tell the life orientation of the bones, and therefore the size of the eyeball, beyond a certain extent.
The certain extent we do have in Velociraptor indicates it may have been nocturnal (and therefore may have had tapeta lucida). This makes sense – it lived in a desert, and the desert is coolest at night.
Okay. Can we extend this to other dromaeosaurs?
The dromaeosaur Microraptor is now well-known for having iridescent black plumage. Lots of modern animals (especially birds) are iridescent; none of these iridescent birds are nocturnal. Again, this makes sense. If you have shiny plumage, it’s probably so other members of your species can see it, and that’s easiest during the day. So we’ve got evidence of Microraptor being diurnal.
Does this mean it didn’t have a tapetum lucidum? Not necessarily. If it evolved from ancestors that had them, they could have been retained, and there are some largely diurnal animals (mostly mammals) today that have tapeta lucida. So this could depend on the lifestyle of the earliest dromaeosaurs. And…here we don’t have a ton of evidence. A lot of the animals around the base of dromaeosauria have display structures that could indicate they were largely diurnal, but it’s not so cut and dry. At the moment we can’t really say if nocturnality was present in early dromaeosaurs, or even in other late dromaeosaurs. At most, we can’t say that they didn’t have them, and in at least some dromaeosaurs they might be justified by some evidence.