Do you know the maximum transactions per second that Litecoin can process with the LN? I searched online, but cannot find the answer. Ethereum is about 20 and Bitcoin is about 3
I guess this number is virtually unlimited
That's likely the reason why you couldn't find any relevant info. Basically, any blockchain is conceptually centralized in respect to processing transactions, i.e. the majority of nodes should accept the mined block to make this transaction valid (read confirmed). This is not the case with LN, since you don't need blocks to send transactions via payment channels, and this basically means that it is meaningless to talk about processing capacity of LN network in terms of transactions per second. Transactions are processed as soon as they reach the receiving end of the payment channel, i.e. they are real time and they are independent of each other as well as blocks found
For Bitcoin, a LN would require a hard fork, correct?
I don't really know
If it requires all clients to upgrade (i.e. old clients won't be able to accept new blocks), then yes, it would require a hard fork (since this is what a hard fork is essentially about). Regarding Bitcoin's roadmap, I guess we should first
activate SegWit simply because LN is a completely new technology which effectively makes Bitcoin into another coin (well, to a certain extent), while SW is just an upgrade which (somewhat) solves current issues (e.g. makes blocks more accommodative)