I'll be working up a comparison at a later date,
based on most likely amounts locked in each of the 3 solutions and how many offchain transactions are really available,
after a glancing look, the thought that thousands of transactions will occur per deposit on LN appears to be extremely overstated except possibility for micro-payments of less than a penny, before new funding is required.

Some preliminary thoughts are a person deposit $200 in their account and spending the entire amount.
Exchange:  1 onchain transaction and possibility a 2nd (optional) onchain transaction withdraw by vendor
Gift Card :  only 1 onchain transaction required
LN          :  2 onchain transaction required per party

In a normal US person, a funding of $200
would allow $40 transaction for gas, $120 transaction for electricity , four $10 restaurant visits =$40

$200 on Exchange , spent on the above
1 onchain to fund account and 1 onchain withdrawl by gas station and 1 onchain withdrawal and 4 onchain withdrawals by 4 different restaurants.

So we have a possible 7 maximum onchain transactions,
however, since withdrawals can be grouped from multiple users at a weekly or monthly basis,
by only withdrawing large amounts, the total onchain transactions can be reduced greatly


$200 on Gift Cards , spent on the above
Only 1 onchain transaction required, the other transactions occur on the gift card network
(For the Purpose of this example the gift card is a Refillable Visa Debit Card accepted at multiple vendors)


$200 on LN , spent on the above
2 onchain transactions Person,  2 onchain transactions Gas Station, 2 onchain Electric Company, 8 onchain transactions from 4 separate restaurants  
6 offchain transactions total

When you look at the above it becomes apparent that gift cards are superior in reducing the # of onchain transactions
over Exchanges and LN.  In the above Scenario :
Gift Cards: 1 onchain transaction required
Exchange : 7 onchain transactions , if none of the companies group their withdrawals with others
LN           : 14 onchain transactions

Just using the onchain blockchain alone and paying the gas station, electric company, 4 separate restaurants directly onchain,
requires 6 onchain transactions.

So anyone really wanting to cut down on the # of onchain transactions would use gift cards over exchanges and LN.  
Other Factors may be more important for the individual on which they choose , but gift cards win decreasing onchain transactions hands down for the normal individual.

You also notice that anyone using LN for normal life purchases such as gas, electricity , restaurants,
end up generating more onchain transactions by trying to use LN offchain network,
than if they just paid the vendors directly onchain.    

FYI:
For 1000 transactions to take place on LN, from a $200 deposit
each transaction would have to be worth no more than 20 cents each offchain transaction.

Which brings up a question, what are people buying that is only worth 20 cents?    
* Even a single 20oz bottle of coke cola is ~$2.00 *

If a person only used LN to buy meals at the same restaurant, of no more than $10 per visit,
you can squeeze 20 offchain transactions out of it, using only 4 onchain transactions, saving 16 onchain transactions,
however if those visits were to 20 different restaurants,
those 20 offchain transactions would be using 40 onchain transactions, a loss of 20 onchain transactions verses paying onchain only.

The above brings an interesting development, LN users that don't consciously plan their transactions to maximize offchain transaction over onchain transactions could actually generate more onchain transactions than if they paid directly onchain and potentially nullify any transactions reduction that LN could have provided.

*Note onchain transactions reduction would still be far more if you used a gift card instead.*