No. Blinds are a separate order and, on a lantern, a considerable one, because a structure with several faces needs a blind for each rather than one blind for the opening. That is worth knowing at the design stage, because the specification of the glass is often the cheaper way to solve the problem the blinds were being asked to solve.
What blinds do generally
The types and what each is for are set out on do roof windows come with blinds.
What follows is what changes when the thing being covered has four or six faces meeting at a ridge.
Why a lantern is harder
Because there is no single plane to cover.
Each sloping face is its own aperture at its own angle, and a hipped end is a trapezium rather than a rectangle, so a lantern blind is a made to measure set.
Individual pane blinds
The commonest arrangement.
A pleated blind is fitted within each glazed bay, running in guides along the bars, so each face is covered separately and the shape of the structure stays visible.
It is the neatest solution and it is a set of units.
How they are operated
Almost always powered, on anything but a small lantern.
Reaching a blind on a roof structure above a kitchen is not practical by hand, so motorised operation from a handset or a wall control is the normal specification.
The control options are on how is an electric rooflight controlled.
Running them together
What makes a set usable.
Grouped on one control, all the faces move together, which is the difference between a system somebody uses and a row of remotes nobody touches.
A single blind across the underside
The other approach, and it changes the room.
A horizontal blind or panel system across the base of the lantern covers the whole opening at ceiling level, which is simpler and hides the structure entirely.
It removes the height that was the reason for the lantern.

Where that suits
A bedroom or a room needing genuine darkness.
Where blackout matters more than the shape of the ceiling, covering the opening at ceiling level is far more effective than individual pane blinds.
Why individual blinds rarely black out
Because of the edges.
Light finds its way past the guides and along the bars, and on a structure with this many junctions a true blackout is difficult.
They are for glare and privacy rather than darkness.
Powered blinds and the cable
The thing to plan at the same time as the lantern.
Motorised blinds need a supply at the lantern, and running that while the roof is open costs almost nothing where doing it afterwards is a chase across a finished ceiling.
It is worth doing even if the blinds are deferred.
What they cost
More than people budget for.
A set of made to measure powered blinds for a lantern is a significant item on its own, and on a large lantern it can approach a meaningful fraction of the lantern.
Where it sits is on how much does a roof lantern cost.
What they fix
Glare, mostly, and privacy at night.
Direct sun falling across a worktop or a screen is genuinely solved by a blind, and a lit kitchen under glass at night is more private with them closed.
What they do not fix
Overheating, to the degree people expect.
An internal blind is behind the glass, so the energy is already in the room, and the fabric then radiates it back.
The mechanism is on do blinds reduce heat through a rooflight.
What fixes overheating instead
Glass and ventilation, decided at order.
Solar control glass stops the energy at the outer pane and an opening face lets what arrives escape, and together they do what a set of blinds cannot.
That is on will a roof lantern make the room too hot.
The cheaper decision
Worth putting plainly.
Specifying better glass at order is usually less than a full set of powered blinds, and it works when nobody is in the room to close anything.

What they do in winter
A small and genuine improvement.
Closed blinds trap still air against the glass, which reduces the loss slightly and, more noticeably, keeps the inner surface warmer to sit beneath.
Fabric and steam
Relevant because a lantern is usually over a kitchen.
Cooking puts moisture and grease into the air, and blind fabric above a hob collects both, so fabric choice and cleanability are worth asking about.
Fading
Faster than on a wall window.
Blinds under glass take a great deal of direct sun, and strong colours fade, so they are a replaceable component rather than a permanent one.
Retro fitting later
Entirely possible and worth planning for.
Blinds can be added years afterwards, and the only thing that becomes difficult is the cable, which is why it goes in at the start.
External awnings on a lantern
The right principle in the wrong place.
Shading outside the glass is what actually stops heat, and on a structure standing above a roof there is nowhere convenient to fix or maintain one.
It is why the glass carries the load on a lantern where an awning would carry it on a roof window.
Cleaning and servicing a blind set
Modest, and access is the issue.
Fabric wants an occasional wipe and guides want keeping clear, and reaching them means working at height inside the room over whatever sits beneath the lantern.
It is worth arranging the furniture with that in mind.
What we want to know on a lantern
We ask what the blinds are being asked to solve before quoting them, because if the answer is heat then the money belongs in the glass and the opening pane instead.
The whole picture is on the roof lantern installation page.
Thinking about this job? We survey across Worthing, West Sussex and the South Downs and give you a fixed price before any work starts, with a 10-year workmanship guarantee.