I have interpreted this question regarding two metrics: usable payload mass to orbit, and total injected mass to orbit – where the latter includes inert stages after burnout.
The highest usable payload mass to Low Earth Orbit goes to the three-stage Saturn V SA-512 vehicle used for Apollo 17. Apollo Project: Exploring the Moon by Robert Godwin gives the mass placed in a 171.3 x 168.9km earth orbit as 311,151lb or 141,136kg. None of the Apollo lunar flights lofted more mass to LEO, although Apollo 16’s SA-511 vehicle propelled a slightly greater payload to TLI (48,617kg vs 48,609kg, where the payload includes the CSM, LM and SLA).
The Saturn V lunar booster is an odd case when it comes to LEO payload. Notably, the LEO payload is the same as the total injected mass. However, the third stage qualifies as part of the payload as it is absolutely necessary for its mission of propelling humans and their spacecraft to the moon.
So, a three-stage Saturn V is not a LEO-optimised vehicle – but a two-stage variant is. The Saturn V SA-513 used to launch the Skylab OWS shows an even greater total injected mass:
http://forum.nasaspaceflight.com/index.php?topic=12519.20 Provides expected masses.
https://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19730025115.pdf Provides expected and actual masses from the flight.
- Skylab OWS = 88,497kg
- S-II/OWS Interstage = 3,453kg
- Dry S-II Stage = 36,654kg
- LOX residuals = 8,324kg
- LH2 residuals = 2,790kg
- S-II other = 2,827kg
- S-IC/S-II Interstage = 4,986kg
The total mass to a 434 x 442km orbit at 50 degrees inclination is given as 147,531kg. Note that the S-IC/S-II interstage failed to separate after being damaged by debris falling off the OWS during the S-IC burn, and yet was still carried all the way to orbit.
MSFC’s Flight Evaluation Report for SA-513 from August 1973 lists the optimal calculated total injected mass as 319,129lb (144,755kg), but this did not account for the S-II interstage failing to separate or, funnily enough, overperformance of the S-IC stage that resulted in 3.9% greater impulse than expected from the first stage.
Discounting the S-II dry mass, propellant and all other stage accessories the SA-513 vehicle’s two stages delivered 91,950kg in the form of Skylab, its fairing and its support structure. Including the S-IC/S-II interstage which was unnecessarily dragged to orbit, this would increase to 96,936kg but is otherwise irrelevant.
Therefore, the record for the greatest total injected mass to Low Earth Orbit by a single launch vehicle is 147,531kg and belongs to two-stage Skylab-1 Saturn V SA-513. This mass was placed into a 434 x 442km orbit at 50 degrees inclination. Of this, 91,950kg constituted the actual payload, while the remaining mass constituted the inert second stage, residual propellant and other accessories.
The record for the greatest functional payload mass to Low Earth Orbit by a single launch vehicle is 141,136kg and belongs to the three-stage Apollo 17 Saturn V SA-512. This mass was placed into a 171.3 x 168.9km orbit at 28.5 degrees inclination. Of this, 48,609kg constituted the lunar spacecraft payload while the remaining mass constituted the partially fuelled transfer stage required for the lunar mission.