How do you want to sweep the source? It's not that clear to me. You could make the source a vsource from analogLib which is a pulse source ramping the value up during the transient; in non-transient analyses it will use the dc value of this source (if supplied) or the time-zero value if the dc value is not supplied.
Or you could use the dynamic parameters capability of tran analysis to ramp up a variable (assigned as the value of the source) over time.
Or you could use parametric analysis to sweep the source separately from the time sweep (this is if you want the sweeps to be orthogonal).
As you can see I'm having to guess a little what your objective is.