Chop the guava into medium chunks and add to a blender. Blend until you get a smooth, slightly coarse mixture.
Transfer to a pot over medium heat and add sugar and lemon juice. Cook for minutes, stirring every minute or so.
Notes
Guava seeds, even when broken down, can leave a slightly coarse texture in the mixture. If you don't like it, you can strain the mixture before cooking it down.
Keep stirring the mixture every few seconds and cook over low to medium heat. High heat will cause the guava paste to end up burning.
The mixture will darken slightly as it cooks, and that's okay.
You can adjust the consistency of the paste to your liking. I stopped cooking it at the 20 minute mark, because I wanted a nice spreadable texture. If you want it to be thicker and more jelly-like, you can continue cooking for a little longer.