What I'd do is send to both places at least while you're coming up to speed on LEM. This will help you use a familiar interface, duplicate what you have in LEM, then cycle out of sending to both when you're comfortable you've got what you need. It might be a week, it might be a while, but it always helps when you have something familiar to base your comparison on.
You should be able to replace your simple alerts in NPM with simple alerts in LEM, and take advantage of features LEM has that NPM doesn't. With LEM, you'll be able to set up more complex thresholds (notify me after X occurrences in Y seconds/minutes), monitor the feed of data in real-time with charts & graphs that also update in real time, use LEM's search to get more insight about the historical data over time, and report on that data in context with other data if you've got needs in that area.
I think only sending the alerts from NPM to LEM (rather than all of the data) will limit the visibility into your data. You'd basically only be sending the ones you know you're interested in, but LEM's real-time monitoring, correlation, and search capabilities would be hindered. Going the other way might make sense once you know what you are looking for - correlating events in LEM and alerting NPM with them.
All of those devices (to my knowledge) do support sending to multiple syslog destinations, so you'll just want to go in and add the LEM appliance as a syslog destination in addition to your existing NPM server.
Just to add my 2 cents (or $20 adjusted for inflation),
I have my traps and syslogs going to both my NPM and LEM. I use the NPM as a trending and a real-time window and use the LEM also for trending but historical review of such. Having it go to the LEM allows me to see a bigger picture when I am troubleshooting an issue or looking for bottlenecks/errors.