As a PPL holder in the USA, what do I need to have on the aircraft (or otherwise?) in order to be able to legally fly at night? LSAs are much cheaper to operate, so it looks very tempting in order to be able to fly more hours, I'm just concerned about getting stuck out at dusk, especially in winter.
Since you have your private, the LSA just has to be approved.
According to the FAA Order 8130.2G CHG 1 which covers LSA certification:
(5) This aircraft is to be operated under VFR, day only, unless appropriately equipped for night and/or instrument flight in accordance with 14 CFR § 91.205, and when allowed by the manufacturer’s operating instructions.
So it must be properly equipped (see below) AND allowed by the manufacturer’s operating instructions. You will need to check this with each manufacturer to see if they certified it for night flight.
91.205 says day VFR instruments (paragraph b) plus:
(c) Visual flight rules (night). For VFR flight at night, the following instruments and equipment are required:
(1) Instruments and equipment specified in paragraph (b) of this section.
(2) Approved position lights.
(3) An approved aviation red or aviation white anticollision light system on all U.S.-registered civil aircraft. Anticollision light systems initially installed after August 11, 1971, on aircraft for which a type certificate was issued or applied for before August 11, 1971, must at least meet the anticollision light standards of part 23, 25, 27, or 29 of this chapter, as applicable, that were in effect on August 10, 1971, except that the color may be either aviation red or aviation white. In the event of failure of any light of the anticollision light system, operations with the aircraft may be continued to a stop where repairs or replacement can be made.
(4) If the aircraft is operated for hire, one electric landing light.
(5) An adequate source of electrical energy for all installed electrical and radio equipment.
(6) One spare set of fuses, or three spare fuses of each kind required, that are accessible to the pilot in flight.