Can Lightning (or other Layer 2 protocols) eventually handle the majority of Bitcoin transactions securely?
To answer your questions, before you can use a Lightning network, there must be a channel. If both parties agrees to spend much Bitcoin, it can support as many transactions but your transaction is going to be limited to the Bitcoin used to open the channel. If you have 100 Bitcoin to spend as small payments, you can spend it in many transactions before they get settled on the main layer but your transaction is going to be limited to the amount used to open the channel and it's secure.
What are the technical limitations that still need to be solved (e.g., routing, liquidity, channel capacity)?
Each you mentioned has their challenges because it's a support layer, not everyone use it, so there is liquidity limit and it's not technical, it's adoption challenge. Routing problems is still liquidity issue because not everyone with channel want to lock all their Bitcoin in a channel.
If Layer 2 becomes the main medium for transactions, will the base layer primarily serve as a settlement layer, similar to how central banks handle reserves?
Hopefully it does, but are you not seeing transaction fees on mempool.space? Some miners are accepting transactions that are as low as 0.1sat/vbytes. If there is no need to open a channel for multiple transactions, it will be way easy to run a transaction and pay some scents on the main layer.
I am curious to know the community’s technical perspective on whether Bitcoin’s long-term transaction scalability will depend mostly on Layer 2 solutions, or if significant base layer changes may still be necessary in the future.
Everything depend on how the mempool becomes congested. If there is a time in future transaction fees becomes higher, there is going to be high use of layer 2, some centralized exchanges support layer 2 withdrawals, some people use it more often than the base layer but if the base layer fee becomes low like we are expecting some wallet supporting txfee< 1sats/vbytes, then layer 2 activities are going to reduce.