Every type of life require a form of solvent to work. Water, Ammonia, Methane, Sulfuric acid etc.
But how about using the Vacuum itself as a solvent?
When visualizing the international working of cells, we often sees different molecules, enzymes and machines floating freely through a transparent background, while the presence of water itself is often omitted. This is known as the Implied Water model.
The presence of a liquid solvent mostly accomplishes these two things: it helps to arrange like structures when it comes to polarity, and it helps molecules to diffuse.
However, self assembly, folding, docking and arrangement of molecules can also happen in a gaseous environment, often needing a (very high) vacuum. For example, molecular beam deposition , plasma deposition/cleaning/synthesis and formation of buckyballs, aerogels, and other exotic chemical constructs. In fact, the original nanobots and molecular assemblers REQUIRES a very high vacuum to even work!
There are two possible routes: diamondoid mechanosynthesis, and gaseous self assembly.
For the first kind of life, imagine the crevices and/or other contacts of a suitable rock/mineral in vacuum: rocks grind away on each other from some periodic force, for example thermal expansion or seismic activity.
Small particles adsorbs a certain molecules, guided by a pattern etched on the rocks, the particle adds molecules in sequence, forming the basic components of life. Now, the patterns themselves could be copied by some other process, for example, a molecule that have a form of connector on both ends, which would work like the needle of a record player, etching the pattern from one crystal onto another, and vice versa. If one of the pattern happens to be the one that makes these replicating pins by some process, it will become more dominant, and this would then produce some error, recruiting more molecules, and starting to assemble components of the patterns themselves. Creating a form of Diamondoid life.
For the second kind of life, think of the Implied water model, but change the "Solvent" space with the actual vacuum of space.
Consider somewhere very hot to keep most materials gaseous, and devoid of any gravity to cause molecules to fall on one side of the container, and this space is filled with a low pressure gas. Now, the molecules within such space could produce three kinds of interaction: Electrostatic, London dispersion and Pi-Pi interactions: the first one causes unlike charges to attract each other, the other two causes like surface to attract each other. The low pressure and high temperature helps the molecules to diffuse across each other, just like a solvent would be for the more "normal" life.
In this space, polymers will radiate heat away, collide with small molecules(gases), and consequently assumes a specific shape, or fold. Vibrational transitions would cool the molecules down, and newly formed polymers will fold. Folded polymers would then catalyze a wide variety of reactions, many known to be happening in a gas phase. One of these polymers consists of units that formed a shape that is complementary to one another, adamantanes, PAHs, and other sort of chemicals that would hydrogen bond. (hydrogen bonds does not(technically) require a solvent)
Some of these polymers would catalyze the polymerisation of the polymer itself through the complementary shape of the molecules, forming the first self replicating molecule within this environment. (Keep in mine that most non-protein solvents within the modern cell have concentrations of mmols to umols a litre, corresponds to pressures of a few hundred torrs of pressure) then, other molecules, then, the first polymerization based molecular assembler (not necessarily the ribosome), encapsulate the resulting mix with some form of polymeric barrier, and you get almost exactly the same sort of life as your everyday cells, with everything from dna analogues to protein analogues, except the implied water background of the cell is replaced with a vacuum (actually low pressure high temperature gaseous) background in zero gravity.