I believe the institutions' hesitancy to use LN is not because of low liquidity. It might be because capital, in the form of Bitcoin, is needed to be "locked" to use the network. Unless there's an incentive or a profit-motive to "lock" Bitcoins in payment channels/provide liquidity, the hesitancy will always be there.
run some scenarios. you can do it for free with a pen and paper or excel
take bitfinex lnd0 with ~11% of the LN network cap (~460btc)
its not the fact that they are putting 460btc at risk into a contract. its the fact that if they had 460btc 'demand' to have withdrawals for people say 10 'hops' away. the liquidity needed on the network to make payments becomes more then the entire capacity of the network
run the scenario (rounded to 450, for lazy math/display)
from
BFX{450:0}H1{450:0}H2{450:0}H3{450:0}H4{450:0}H5{450:0}H6{450:0}H7{450:0}H8{450:0}H9{450:0}H10
to
BFX{0:450}H1{0:450}H2{0:450}H3{0:450}H4{0:450}H5{0:450}H6{0:450}H7{0:450}H8{0:450}H9{0:450}H10
just to move 450 from BFX to H10 level channels requires the whole network to have liquidity of 4.5k
thats 4.5k just to fulfil payment needs of just 450
i hope you can atleast 'observe' and acknowledge this basic LN concept: that say(for one example) hop3 people not using their channel just for themselves(their own personal payment) but instead having their funds used by others..
and after that. Hop3 level people (for one example) have nothing spare to pay hop4,5,6,67,8,7,9,10 because its already used up by BFX
do you 'observe' yet?
aside from that are the MANY variables and flaws that are involved where not all hops have the equal amounts to even be able to fulfil payments.
but if you can first understand the liquidity concept. then you can move onto deeper scenarios of other problems large institutional services face.. and you might then be able to 'observe' why the el-salv chivo service dropped LN late last year just months after trialling it