Solar -> Charge Controller -> Lithium -> DC-DC Charger -> Lead Acid -> Load
The load is always pulled from the lead acid, but in reality if the load increases your DC-DC charger will just put out more juice (until it hits its limits) and not really drawn down the lead. If you max out the DC-DC charger yeah you'll start to draw from the lead but that is ok - that is what it is there for.
For a really large bank that you need to draw down lots of amps you may need to rework things, but likely lead acid doesn't work for you in those cases anyway. This works for banks where your load is like 50 amps or less. For my case, I have 1kAH including the lithium and I do not ever draw more than 20 amps. Works great.