Lupin's werewolf transformations would have interfered with him becoming an Animagus.
Becoming an Animagi is a long process which requires things to be done on a daily basis, including nights of a full moon.
Talent in both Transfiguration and Potions is necessary to become an Animagus. No responsibility can be taken for any physical or mental problems resulting from following these instructions.
For the space of one entire month (from full moon to full moon), a single leaf from a Mandrake must be carried constantly in the mouth. The leaf must not be swallowed or taken out of the mouth at any point. If the leaf is removed from the mouth, the process must be started again.
Remove the leaf at the full moon and place it, steeped in your saliva, in a small crystal phial that receives the pure rays of the moon (if the night is cloudy, you will have to find a new Mandrake leaf and begin the whole process again). To the moon-struck crystal phial, add one of your own hairs, a silver teaspoon of dew collected from a place that neither sunlight nor human feet have touched for a full seven days, and the chrysalis of a Death’s-head Hawk Moth. Put this mixture in a quiet, dark place and do not look at it or otherwise disturb it until the next electrical storm.
While waiting for the storm, the following procedure should be followed at sunrise and sundown. The tip of the wand should be placed over the heart and the following incantation spoken: ‘Amato Animo Animato Animagus.’
The wait for a storm may take weeks, months or even years. During this time, the crystal phial should remain completely undisturbed and ...
[there are a total of ten steps listed]
Pottermore - Animagi (behind paywall)
Seeing as Lupin's furry little problem would keep him otherwise occupied during these times, he would not be able to become an Animagus.