Need an alert generated for successful and unsuccessful login attempts to LTM management interface

I haven't personally worked on the Big-IQ, but on the LTM modules its doable. You'll have to set up snmp trap alerts. Find the log format, define it in user_alert.conf, once the log is found, alert will trigger and action is performed.

Without reinventing the wheel, follow these 2 links, you'll be able to achieve your task.

K3667: Configuring alerts to send email notifications

Refer  post in Email alert for failed and successful login

Keep us posted on the progress !