Opening a payment channel requires an on-chain transaction, as does finalizing a sequence of transactions sent over the channel. So for every sequence of off-chain transactions on a Lightning Network, you must put two transactions into the blockchain.
Thus you need to make more than two transactions in a sequence before moving them off-chain can offer any benefit, either at the micro scale (in the parties' cost of transacting) or at the macro scale (to Bitcoin's aggregate transaction throughput, both on- and off-chain). In theory a sequence of transactions done over the Lightning Network can involve multiple recipients and be routed among many parties, however, so a sequence of off-chain transactions need not be a sequence of recurring payments in the usual sense.
Whether a Lightning Network offers any cost or scaling advantage, and how big those advantages might be, will depend in practice on (a) whether good methods can be found to route off-chain transactions between hubs and end-users of the network, and on (b) the statistics of the real-world patterns of transactions that people end up using the network for.
Personally, I think that unless Lightning Networks give rise to major new classes of transactions (e.g., micropayments), then we are unlikely to see any significant scaling win from them any time soon. There is a classic chicken-and-egg problem of gaining a critical mass of users, which will take time to overcome, and people today typically use Bitcoin fairly infrequently, which makes the two-transaction overhead to get in and out of the payment channel significant relative to the likely size of off-chain transaction sequences.
The question is what alternatives exist, and which will gain traction, in the case that on-chain capacity remains severely artificially constrained and on-chain fees continue to rise. Maybe people will switch rapidly to Lightning Networks, or maybe they will switch to altcoins, or maybe they will just stop using cryptocurrencies altogether (or never start). We'll see.