In transport category aircraft there has to be an alternative mechanism to extend the gear if the normal mechanism fails, but there is no requirement for an alternative retraction mechanism. This is required e.g. by EASA CS-25 (Certification Specifications for Large Aeroplanes):
(c) Emergency operation. There must be an
emergency means for extending the landing gear in
the event of –
Any reasonably probable failure in
the normal retraction system; or
The failure of any single source of
hydraulic, electric, or equivalent energy supply.
(EASA CS-25.729 - Landing Gear - Retraction Mechanism)
A common solution to implement this alternative extension is via gravity. There is usually a way to mechanically release the up-locks and shut off any hydraulics to the gear from the flight deck, which will result in a gravity gear extension, e.g. in the Boeing 737:
2 Manual Gear Extension Handles
Right main, nose, left main – Each landing gear uplock is released when related
handle is pulled to its limit, approximately 24 inches (61 cm).
(Boeing 737 NG FCOMv2 14.10.3 - Landing Gear - Controls and Indicators)
The reason why no alternative retraction mechanism is required, is that there is simply no need for it. Should the gear fail to retract after takeoff, the pilots can just land again, either at their departure airport or somewhere else (possibly after burning / dumping some fuel if the aircraft is above its maximum landing weight). Continuing the flight to the destination is usually not a good idea because the landing gear extended results in a large increase in drag and therefore requires significantly more fuel (see e.g. Hapag-Lloyd Flight 3378).
In the accident you linked (LOT Flight 16), the alternate gear extension mechanism was also unavailable due to a tripped circuit breaker:
On Dec 18th 2017 the PKBWL released their final report concluding the probable causes of the accident were:
Failure of the hydraulic hose connecting the hydraulic system on the right leg of the main landing gear with the center hydraulic system, which initiated the occurrence.
Open C829 BAT BUS DISTR circuit breaker in the power supply circuit of the alternate landing gear extension system in the situation when the center hydraulic system was inoperative.
The crew’s failure to detect the open C829 circuit breaker during approach to landing, after detecting that the landing gear could not be extended with the alternate system.
(avherald.com, emphasis mine)
The alternate landing gear extension in the Boeing 767 (as used by LOT 16) is also a gravity extension, but unlike the 737 the up-locks are released electrically rather than mechanically from the flight deck:
Landing Gear Alternate Extension
The alternate landing gear extension system uses an electric motor to trip the
locking mechanism for each gear. Selecting DN on the ALTN GEAR EXTEND
switch releases all door and gear uplocks. The landing gear free-fall to the down
and lock position.
(Boeing 767 FCOM 14.20.2 - Landing Gear - System Description)