Use Lag Operator to find Lifetime Budget Constraint The budget constraint is 

$c_t + \tau_t + s_{t+1} =w_t(1-l_t) +(1+r_t)s_t$

And assume

$\underset{t \longrightarrow \infty}{lim} \ \displaystyle{\frac{s_t}{\Pi_{i=1}^{t-1} (1+r_i)}} = 0$

Lag Operator $L$ is defined as $L \cdot x_{t+1} = x_t$

How can I get lifetime budget constraint using the Lag Operator?

Many Thanks!
@T. G.: I think I obtained the expression for $s_{t+1}$ as a function of the other variables. I don't know what lifetime budget really means so I'll write the answer here and hope it's useful.

$s_{t+1} = \sum_{t=0}^{\infty} \lambda_{t} (w_{t}(1-l_{t}) -c_{t} - \tau_{t})$ 

where $\lambda_{t} = \prod_{i=0}^{t-1} (1 + r_{t-i})$.

I'm not certain if it's correct but intuitively, it looks like exponential smoothing of some kind of expression each period, except that the smoothing constant is not constant and is a function of the past interest rates ??