Frequency-ratio at baseband IQ-mixing
that's pretty simple: in digital domain, real-world frequencies have no inherent "meaning". 

That is, a period of a real-world sine of frequency 10 Hz might be 2, 200, 1233 or whatever samples long, depending on the sampling rate.

Thus, periods in DSP can only be measured in samples; for example, a sine of period 1 second has a period of 5.4 samples if the sampling rate was 5.4 S/s.

Now, logically, that also means that frequencies can only be related to the sampling rate. Hence, your $\frac{f_{LO}}{f_\text{sample}}$ (which is a unitless thing!) oscillator corresponds to an analog oscillator of frequency $f_{LO}$ (which has Hertz as a unit).

With your question in mind, it strikes me as odd that you're looking at a figure describing a receiver that mixes in the digital domain – in software defined radio, most receivers try to minimize the rate at which the ADC needs to run, simply for cost, efficiency, complexity, ADC dynamic range, and noise bandwidth reasons, and thus have the IQ mixer on the analog side – I'd call your design a bit of a "speciality". So, if this is you learning about direct conversion receivers, you might have picked an unlucky reference. If this is you learning about different types of digital receivers: That is extremely close to the theoretical perfect Software Radio, that does all the signal processing in digital domain.

Also note, in the figure, $f_s \overset !\ge 2\cdot f_{max}$ of the low-pass filter, not only one time that frequency (I assume "GHz" just means "order of magnitude is Gigahertzes"). That's why direct sampling is really an expensive technology for high-frequency signals (and why undersampling with filters or an IF makes a lot more sense, most of the time, since you don't care about everything happening between 0 Hz and the maximum frequency of your signal of interest, usually, but only about some limited bandwidth around a center frequency).