Probably, everything was said already but not by everyone. So, here is my turn: =)
For the sake of completeness, we should clarify what we are talking about. I try to put it short and comprehensive, so please forgive inaccuracies.
Firstly, we are talking about RNAV (Area Navigation) which is satellite based navigation (GNSS, for example GPS, GLONASS etc), nowadays mostly improved by corrective information provided by ground stations, satellites or the like (GPS: ABAS, GBAS or SBAS) in contrast to conventional “raw-data” navigation using ground stations. The term “RNP” (Required Navigation Performance) is also used in this context and describes the requirement of the on-board avionics to meet a certain degree of precision in order to be allowed to fly certain procedures. The degree of performance required might, for example, be 0.3 (RNP 0.3), which means that the on-board avionics must be within 0.3 NM from the actual position for at least 95 % of the time. In real life, there is the ANP (Actual Navigation Performance) indicated on most avionics. This piece of information basically tells the pilot whether he is allowed to fly certain approaches or not.
As to LNAV and VNAV: Again, it is important to know what we are talking about. LNAV and VNAV are mostly (with the exception of RNP approaches, see below) associated with autopilot modes. LNAV means that the AP/FD follows the flight plan left/right), VNAV means that the AP/FD considers the altitudes/flight levels provided in the flightplan.
VNAV mode does not necessarily mean that altitude information is derived from satellites! VNAV mode basically is only a method how the autopilot calculates the required climb/descent rate for meeting a defined altitude/flight level at a specified waypoint.
For the sake of completeness, LNAV/VNAV might also relate to RNAV (RNP) approaches:
As stated above, RNAV/RNP always relies on (lateral) positioning derived from signals coming from satellites and interpreted by on-board avionics, improved (augmented) by correction signals coming from ground stations, geostationary satellites or the like. When it comes to approaches, it is obvious that there is a very high degree of precision required in order to provide safe instrument approaches, in particular with regard to the vertical guidance. This is, where the terms “LNAV”, “LNAV/VNAV” and “LPV” come in - with regard to approaches.
To put it short:
“LNAV” approaches have about the same precision and minima as VOR approaches: No vertical guidance (from the FAF onwards) at all but only check altitudes on the approach plate to monitor whether you are above or below the intended glide path.
“LNAV/VNAV” approaches are similar to ILS Cat I approaches when it comes to precision and minima. There are both vertical and lateral guidance, however, the vertical guidance can take the information from the barometric altimeter into consideration (similar to ILS Cat I). Therefore, the minimum is quite high.
As someone else already stated, “LPV” means “Localizer Performance with Vertical guidance” and is the most precise approach available when it comes to RNP. If I recall correctly, vertical information in this case is indeed taken from satellite based information. Minima can be below Cat I minima.
For example, the RNP approach into RWY 28R in LOWK provides for different OCAs (Obstacle Clearance Altitudes), which are the basis for the Decision Altitudes, whether your aircraft is capable of LNAV, LNAV/VNAV or LPV: (see LOWK RNP 28R)
Again, please note that this is only a question of the avionics’ capabilities and has absolutely nothing to do with autopilot modes!