How much computing power is required for that?
The computing power required to brute force private keys is incredibly immense, so much so that the human mind cannot consider its largeness.
Let's assume that you have a processor (say an Intel Xeon) that can perform 1 Trillion key guesses per second. The number of keys possible (and thus the number of keys that you would have to guess in order to guess a private key) is
2^256. With 1 trillion guesses per second, that single processor will take
3.671743 * 10^57 years, which is
2.7 * 10^47 times the age of the universe.
Now if you wanted to have enough processors to get a "reasonable" time frame of 1000 years, you would need
3.671743 * 10^54 processors. With Intels biggest Xeon Platinum chips at 7.6 cm X 5.6 cm, this many chips would take up
1.564162518 * 10^55 Square Meters just to lay them all out (not even on motherboards or the rest of a computer required to even have these processors be useful). With this much area, you could cover the Sun
2.564 * 10^36 times.
Even with more efficient ASICs and processors that can do more key guesses per second, the immense-ness of these numbers makes it so that the numbers barely change; they are still incompreshensibly large.
Does any hardware exist which can find a matching private key in, say, a year?
No, if there were, then Litecoin's signing algorithm would be considered broken.
Is it possible that it ever becomes cheap enough to bruteforce Litecoin addresses, i.e. it costs less money than one can steal from the address once the key is found?
It is possible, but not through brute force. Making it cheap enough requires a cryptographic break. Currently, the only known solution to finding someone else's private key besides brute forcing is to use a quantum computer with several thousand qubits. Such computers do not yet exist.