Pollard's Lambda algorithm ecdlp with Pohlig Hellman
If the question is "can I solve the ECDLP by combining Pohlig-Hellman and Pollard's lambda", then the answer is yes, provided your $p-1$ is smooth enough.

First off, as mentioned in the comments, a search interval of $[0, 2^{40}]$ is quite doable with Pollard's lambda.

Factorize $p-1$ to get all the $B$-smooth prime factors; let's say there are $k$ of them, the ${r_k}$. Then run Pohlig-Hellman on each of them and obtain the secret key mod $r = \prod_i^kr_i$. If the order of your base point on your curve is $Q$, then your search interval looks like $[0, Q/r]$. So $Q/r$ puts the bounds on how long you would expect the lambda algorithm to find a collision. 

What's a good $B$ for smoothness? Now this is implementation-dependent, so that depends on what you're working with and how long you have to wait. In practice, I found that if you factorize $p-1$ up to about $2^{20}$, and you have a few primes of that size, and the order of your base point is much smaller than $p-1$, that cuts $Q/r$ down to a reasonable size, but of course your experience may differ.