Where a monster lives is important to any story involving it, even if its home is never shown. What it takes with it from there, how far away it travels, and what it takes home will affect our uses of the monster. Showing its home gives us an opportunity to characterize the monster, while avoiding doing so, or just giving hints, helps create mystery about it.
Our monster may not have a lair, but the nature of monsters in literature has typically been cautionary, meaning those living near it are supposed to learn something about themselves from the existence of this monster. We don’t have to follow that, but a monster that goes away for good may prevent a population from learning anything about themselves. On the other hand, traveling monsters provide new opportunities, even across other planets.
There’s no reason our monster can’t have access to easier means of getting around, such as a magical device or a portal near its home which it stumbled upon. For SF, a monster with access to an interstellar ship is very useful, and we can either have that ship be the monster’s lair or function like a home away from home. Possible justifications are either that the monster was on a ship when it became a monster, or that a ship landed near it and it ended up onboard, likely killing the crew after launch.
A lair can include treasure, weapons, and the remains of victims, all of those being fairly standard furnishings reminiscent of Medusa’s lair from Greek mythology. The bones are more likely from two occurrences—feeding on species or animals, and/or defending itself with the resulting victims left there. This is one reason to decide on our monster’s tastes. And if our monster leaves dead bodies around, this says something about it, whether that it doesn’t care about the smell, wants to send a message to visitors, or doesn’t have a clue about disposing of bodies. It might also be unaffected by any disease this could spread.
The mystery of where one lives often occupies stories to the point of being a cliché, and yet it is such an obvious concern that it’s nearly inevitable for characters to search for the lair. Rather than avoid this, make your search and discovery worthwhile. While a lair is often hard to find or reach (or escape from alive), making this impossible lessens the usefulness of our monster.
To aid this, decide what kind of evidence the monster leaves when it’s away from home. Are there trails or footprints leading back? Does it cover its tracks? Are spores left behind? Does it kill and leave remains or take anything with it, particularly something (or someone) valuable and which compels action to thwart it? Is the trail it leaves a trap? Is magic (in fantasy) or special tracking equipment (in SF) needed? Does it have the ability to thwart some measures?
Knowing whether our monster is nocturnal or not will figure into any stories. Things awake and prowling at night are more intimidating, but there’s no reason it can’t be active during the day. The effect on a population terrorized by it becomes all encompassing, for they’d still fear it more at night, just because humans, at least, fear the dark. Our monster’s enemies will have some sense of its schedule and will plan their attacks for when it’s sleeping, if they know its lair. If they don’t, they’ll be trying to trap or otherwise attack it when it’s on the prowl.