First off get out of the CL
Assuming it's at least year 70 (they should be out in 68, but Firesoul changed them for some reason)
And of course assuming you're using OP+4.0, -not sure what the YFA is on the taldren stock shiplist
Grab a CWLP/DWLP /CWP or even move into a CA or CC (whatever you can find that has the most power- there could be a couple of them depending which shiplist you're using- Lyran ships tended to upgrade power, so the one with the most power is usually the latest)
Lyran ships to avoid are the FF,CL and to a lesser extent the DD (and of course all derivatives)
The FF's favoured Disrupters over the esg's ,the CL's were just generally lacking in everything
(power,weapons,turn mode,shields,internals) and the DD's were not much better.
The main thing to concern yourslef with is to remember the ESG uses a capacitor like phasers.
So when it is charged- you don't have to worry about it (unlike the Disrupters of course)
And it's generally best to have a higher maneuverability ship to be able to hit the enemy on whatver shield you want to hit them on. (Cl has a C turn mode, CW's have a B, DW's have an A)
With Lyrans it is really about the power though, they go from being one of the most power starved races to one of the one's with the nearly the best power ratio on most of their ships.
The DWLP (for example) shouldn't really get hit with a med speed drone -ever.
With an A turn mode and the ability to power all it's weapons at spd 24 you should bea ble to dance around any of them- even if fighting a human opponent.