I'm confused about how massless particle is influenced by gravitational force. Some source point to the energy conversion to mass and vice versa so light is treated similarly, other source mentioned "space tells light how to move" eliminating the need for a particle to have mass. What is the correct explanation that explains how gravitational lensing works? (Don't tell me duality, the unique properties of light and this question is from a 3 yrs old liar.)
Mass curves space.
However light follows the path of least distance between point A and B. The path of least distance on a flat surface is a straight line.
However if you consider a 2 dimensional surface then put a dent pushing it into the 3rd dimension - the shortest trajectory from point A to B across this dent changes from a straight line to something which appears to curve around the radius.
The shortest path in general from point A to B is called the geodesic. Sometimes this is called the straight line in curved space. https://en.wikipedia.org/wiki/Geodesic
So extending the idea to three dimensions rather two you will need to make a dent into the fourth dimension. The end effect will be something that would look like the image below but you rotate the plane surface about the axis of symmetry - consequently light is spread around the radius entire massive object.
Gravitational lensing in 2 dimensions. The observed position is ignoring the fact that the light was travelling across curved space! Source: http://davidjarvis.ca/dave/gallery/lg/gravitational-lens-01.jpg