@mjfwv:
Please define "run".
What lithium battery? (chemistry / brand / type / size / # of cells in series or parallel)
What DC battery? (same)
If with "run" was meant "discharge" (use), then YES. For example with a diode in series of each battery & using batteries with roughly equal voltage & current capability. This has some drawbacks though - therefore more details needed.
If "direct connect, charge and discharge" was meant, then NO. Different chemistries need different charging methods. Serious troubles may result if eg. lead-acid or NiMH charging method is applied to Li-ion battery. Differences in voltage / capacity / current capability only makes this worse.
In general if 1 battery doesn't suffice then a) use a bigger battery, or b) use more of the same batteries in series or parallel.