Mini-Circuits also makes amplifiers for 500 MHz signals.The Mini-Circuits passive (2 transformers and 4 diodes) double-balanced mixers DBM's have three ports: RF, LO, IF. All three ports expect 50-ohm source or load. Look at the schematic of the double-balanced mixer. You apply your small 500-MHz signal to the RF port. You apply your large local-oscillator signal to the LO port. The synchronous-demodulator output appears on the IF port. The IF port is DC-coupled, though it may have a few millivolts of DC offset due to mismatch among the 4 diodes and due to asymmetry of the LO signal.Analog Devices does make DBM's for use at 500 MHz. Study their datasheets for DBM's and for IQ (In-phase and Quadrature) mixers.
The DC offset of the DBM output limits the small-signal effectiveness of the lock-in amplifier. Gain before the DBM reduces this problem but also reduces the large-signal dynamic range.You can eliminate the DC offset by making your LO generate both I and Q LO 10 kHz away from your signal, using two mixers to give you I and Q components at 10 kHz. Run these into a stereo audio A/D converter (ADC), and do the final synchronous demodulation in software, where DC offset is tiny numerical round-off error.
You could also run your 500-MHz signal into an RF ADC running at 2 GSPS, and do the synchronous demodulation in an FPGA.The oldest reference I know of to IQ demodulation to a complex signal in the modern sense, is D. K. Weaver's paper, "A Third Method of Generation and Detection of Single-Sideband Signals", pages 1703 to 1705 in the December 1956 issue of the Proceedings of the IRE (now the IEEE). Modern DSP'ers will find Weaver's method remarkably familiar.