There are actually fewer Ls than Bs, but they're somewhat less in demand. It's very canton-dependent. Some cantons never use L instead of B for permanent contracts, and really follow what their purpose is supposed to be according to the law. Some (including mine) literally have it codified in their rules that you cannot get B until after you've had L for two years, even with a permanent contract (at least it's clear). Some fall in-between and might give L or B depending on the state of their quota allowance...
Should you get your permit to live/work here your banking choices will be severally restricted due to the US’s FATCA law. Still since you are currently in the UK I assume you’ve come up against this already. UBS, Credit Suisse and PostFinance are likely the only banking options you’ll have here; none of the other banks are likely to want to take you on.