The upgrade paths from 14.04 LTS were to
- 14.10 (ie. off the LTS path), or to
- 16.04 LTS.
Both of these paths are gone because both are now EOL (end-of-life). FYI: Lubuntu releases use a year.month format so 14.04 means you have/had the 2014-April release which had 3 years of supported life, reaching EOL 2017-April
Lubuntu up to 18.04 LTS used the LXDE desktop, and Lubuntu 18.04 LTS is the only release that is still supported using that desktop, so a re-install of that release is possible.
If you want to go this way (stay with LXDE), I’d recommend backing up your data of course, validate & boot 18.04 install media; install using “Something-else” using your existing partitions ensuring you don’t have format selected. The installer will note your installed packages, erase system directories, install system, add-back your additional packages (if available in 18.04) without touching any of your user files unless you had the ‘format’ box checked.
The same mentioned for 18.04 LTS can also be used with 19.10 (except ‘Something-else’ is called “Manual Partitioning”), however its results won’t likely be as clean as a re-install and restore of personal data as wxl suggested.
The primary benefit of Lubuntu 19.10 (even though a normal cycle with only 9 month life) is it will allow easy upgrade to Lubuntu 20.04 LTS when available; the 18.04 option lacks that. It’s also more modern, is what the current Lubuntu manual is geared for (https://manual.lubuntu.me/) and other secondary benefits too…
If your box/machine is x86 (32-bit) only however, Lubuntu 18.04 LTS is your only option.