Usually, the direction is not mentioned as it is fairly obvious which direction a player is travelling, and along which line. Technically, when definition #3 is mentioned, a direction must be specified.
The three different definitions of LV all interact. For instance, it is possible for a player to gain LV and reduce that on the line correspondingly, or vice versa, provided that both LVs remain positive and in the same direction. An LV in the 'wrong' direction is considered to be negative, and therefore requires a reverse and consequent token expenditure.
LV is also gained in some variants of the game by moving away from 'higher' stations or towards 'lower' ones (and lost in the converse way.) (See high station.) LV may be gained or lost during loop procedures due to the natural gravitational effect of stations and token stacks (which of course add to the weight of the station.)
If the overall LV (meaning #3) is altered, then that alteration is passed on in strict proportion to all the Underground lines. (Thus, if the overall LV is halved, then the LV on all lines is halved.)