If you've created a trigger and it is not properly using the Infusionsoft lead owner you need to check your Infusionsoft Settings.
You can find this by heading to your avatar on the far left of the app and clicking:
Settings > Integrations > Vertical Ellipsis
Once you're inside your Infusionsoft Settings it should look like this:
Inside your Infusionsoft Settings, you can map Infusionsoft Users to Salesmsg Users.
Adjusting this setting is important because this is how the Trigger knows who to assign your text messages to when you use the Infusionsoft Lead Owner function.