Well, you could replace your lifeform with a robot. If you have a machine ecology, as in James P. Hogan's Code of the Lifemaker, it might be arguable that there is no metabolism, and your range of energy source options becomes much wider.
But machine ecologies aside....
Option 1: Sunlight. Obviously, in a place as cold as Triton, this will be a much scarcer resource than it is on Earth (after all, it's the relative lack of sunlight that makes it so cold in the first place!), but its not completely absent. Cryogenic "plants" living on or near the surface could easily get some of their energy (or even all of it, if they grow very slowly) from sunlight, converting it into chemical energy which can then be exploited by herbivorous animals just as happens on Earth.
Option 2: Geothermal heat, from a combination of primordial heat of formation, internal radioactive decay, and tidal heating of the host body. There is the Earth-analogue route, where you expect cryovolcanic areas to produce energy-rich molecules which can be directly exploited by lifeforms, but an LN2 environment opens up some exotic new options--native lifeforms could directly exploit temperature gradients around cryovolcanic sites to generate electrical charges which can then be used to power metabolic processes.
Option 3: Cosmic rays, via free radicals. Radiation from space impacting the surface ice would dump some of their energy in the breaking of chemical bonds and formation of free oxygen and nitrogen ions, and other high-energy compounds. "Cryofungi" and cryoplants could exploit this resource by growing roots / mycelia through the "soil" to soak up enery-rich molecules.
Option 4: Direct exploitation of nuclear energy. Organisms could concentrate small quantities of radioactive materials in their bodies and capture the radiation for energy directly. Beta emitters can be used to create charge gradients directly (like in nuclear beta batteries); alpha emitters probably could be exploited to do the same. Gamma emitters could be sequestered within cages of gamma-absorbing pigments to power "photosynthesis"--and there are real-world microbes and fungi that actually do use melanin as a photosynthetic pigment for capturing x-rays and gamma-rays!
(Last two options partially stolen from Robert Forward's Camelot 30K.)