1- Most of the manoeuvres are coplanar orbits '' Including The Hohmann transfer''.
2- ''Your what (if) question: L point is one one the Lagrange points., however your question is more related to what we call the restricted three body problem, in this case we consider a system of three bodies, such as sun, earth and a space craft '' satellite for example'', or moon, earth, and the space craft. In this case the mass of the space craft is astonishingly small compared to the primary masses ( earth and moon, or sun and earth). Here we need to find the equations of the motion of the secondary mass (space craft) relative to the primary masses (sun and earth, or earth and moon), establishing the position vector of the secondary mass relative to primary masses.
2.1: Lagrange point: For the fact that the equations of the space craft have no closed form of analytical solution, so one can use them to find the location of equilibrium points, these point are the location in space where the secondary mass would have zero velocity and zero acceleration, which means the secondary mass appear permanently at rest relative to earth and moon system , or sun and earth system...So here one needs to find the equilibrium points ( also called liberation points, or Lagrange points). For example in the earth-moon system the five Lagrange points orbit the earth with the same period as the moon. Can you tell me why?
Important remarks about what we call Lagrange points,or equilibrium points:
2.2 if an equilibrium point is stable, then a small mass occupying that point will tend to return to that point if nudged out of position. The perturbation result in a small oscillation(orbit)about the equilibrium point. Thus object can be placed in a small orbit called (halo orbits) around stable equilibrium points without requiring much in the way of station keeping. On the other hand, if a body located at an unstable equilibrium point is only slightly perturbed, it will oscillate in a divergent fashion, drifting eventually completely away from that point. It turns out that Lagrange point L1, L2, and L3 on the apse line are unstable, whereas L4, and L5
60 degrees ahead of v and behind the moon in its orbit are stable. However L4, and L5 are destabilized by the sun's gravity.......
For example Solar observation spacecraft have been placed in halo orbit around L1 point of the sun-earth system. L1 lies about 1.5 *10^6 kilometers from the earth and outside the earth's magnetosphere.Example of such mission The international Sun-Earth explorer 3 (ISSE-3) launched in August 1978; the Solar and Heliocentric Observatory ( SOHO) launched in 1995, and the advanced composition explorer (ACE) launched in August 1997.
2.4: I think one needs to do some reading about Halo orbit....and the restricted three body problem, (Circular and elliptic).
2.5: I will suggest to read the following: Non-hohmann transfer with a common apse line . There are a lot interesting books.........