You can always check in the current FAR/AIM and don’t forget that MEL on the aircraft.

Stay out of the trees!
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FAR/AIM

But I am pretty sure you only need the three position lights on the wingtips and tail. As well as at least one anti collision light. This can be either strobe lights or a flashing or rotating beacon. Most of the 172′s I have been around have the regular nav lights as well as a flashing beacon on the top of the tail.
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The answer is no, not necessarily as long as you comply with 91.205(c) and 91.209
91.205(c) says you must have 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.
Part 91 GENERAL OPERATING AND FLIGHT RULES
Subpart C–Equipment, Instrument, and Certificate Requirements

Sec. 91.209

Aircraft lights.

No person may:
(a) During the period from sunset to sunrise (or, in Alaska, during the period a prominent unlighted object cannot be seen from a distance of 3 statute miles or the sun is more than 6 degrees below the horizon)–
(1) Operate an aircraft unless it has lighted position lights;
(2) Park or move an aircraft in, or in dangerous proximity to, a night flight operations area of an airport unless the aircraft–
(i) Is clearly illuminated;
(ii) Has lighted position lights; or
(iii) is in an area that is marked by obstruction lights;
(3) Anchor an aircraft unless the aircraft–
(i) Has lighted anchor lights; or
(ii) Is in an area where anchor lights are not required on vessels; or
(b) Operate an aircraft that is equipped with an anticollision light system, unless it has lighted anticollision lights. However, the anticollision lights need not be lighted when the pilot-in-command determines that, because of operating conditions, it would be in the interest of safety to turn the lights off.
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