That’s what hwe said
Ubuntu’s Hardware Enablement (HWE) stack is a set of packages that provide a newer kernel and video drivers for Ubuntu’s LTS releases. These are released every six months using backported packages from the development Ubuntu releases. So sometime after October the 18.04.4 HWE will be released, based on Ubuntu 19.10. The HWE stacks work on Ubuntu derivatives such as Mint, so if you think new drivers might solve some issue that’s denying you the Perfect Install you were promised, it’s worth trying.
The converse is also true: if you aren’t having hardware issues then installing the HWE stack could result in breakage. The new packages aren’t as thoroughly tested as the rest of the LTS package base, so you could end up creating new problems by installing these. With that caution in place, the following will give you all the LTS goodness:
$ sudo apt install --install-recommends linux-image-generichwe-18.04 xserver-xorg-hwe-18.04
At the time of writing, that will get you a 5.0 series kernel, as opposed to the 4.15 line that the LTS release will stick to. It’s worth noting that features, besides bugs and security fixes, do get backported into the Ubuntu kernels, so numbers don’t tell the whole story here. But such support is added much more conservatively and is subject to more scrutiny than the HWE packages. If you really want to break things there’s also a hwe-18.04-edge kernel package, which contains bleedingedge updates.