I have a bottleneck affecting traffic. There are 4 switches with each of them running a line to the next to provide internet. I haven't played around with LACP LAG too much and am wondering if the setup in this diagram would work. I am wondering if this would help my bottleneck between the switches.
The setup is totally valid, provided all devices support LACP LAG.
Two things though:
The network design is not very good, neither for reliability nor from the performance/efficiency perspective. Basically, don't chain but build a tree. If possible, connect the top three switches to the bottom one directly (or even the firewall), shortening forwarding paths, removing dependencies, and removing the bottleneck from the interconnects.
Note that aggregating links does not work like a single interface with the aggregated speed. Instead, each member switch uses an algorithm to select a physical link for each frame, so that similar frames always use the same link. Depending on the switch algorithm, the criteria can be source/destination MAC addresses, IP addresses, or IP addresses and TCP/UDP port numbers.
So basically, the more flows run across a LAG trunk, the more likely it is that they distribute evenly across the physical links. Few flows are not likely to distribute well unless you fine tune the mentioned criteria.
If changing the topology isn't possible and the bottleneck at the bottom switch is hard to remove, using multiple VLANs with MSTP may be an alternative. Grouping the VLANs into several MSTP instances that you can then run over their dedicated interconnects allows you to guarantee bandwidth for the topmost switch which isn't (easily) possible with simple LAG trunks. If this is feasible depends on your workloads and their distribution across the switches.