Glad it worked out. For anyone playing along at home, this would also work within SymPy.jl:
v = sympy.Piecewise(
(l1, Gt(t, 0) & Gt(1, t)),
(l2, Gt(t, 1) & Gt(3, t)),
(l3, Gt(t, 3) & Gt(4, t)),
(0, true))
plot(v, -10, 10; le=:step)