Combat Lina is actually pretty good, her attackpoint is awful early game though and farming with spells isn't very reliable unless you're mid and bottle crow or somehow control the runes. Assuming you do farm and people let you, it's pretty strong, skip leveling the stun to focus on the passive(1pt stun obviously but duration doesn't increase and you can do without the dmg), get phase boots for the raw damage then I'd probably go for drums for some health, or casual pointbooster(for an agh later) and then into maelstrom then bkb/mkb/crit/lifesteal/whatever are fine choices.
Mostly the issue is finding a team that'll let you farm with a lina but once farmed it's pretty strong if you weave your spells to keep the fiery soul buff up as she has long range and laguna blade is a pretty fucking good "carry" spell.
That said you could go traditional caster lina and if you happen to be farmed convert later on, kinda like how QoP does sometimes. For this the best item I feel to start with would be an orchid or a sheepstick(but straight sheep is ballsy due to the high cost on the parts) into a bkb maybe and then crit/mkb to mix it up.
Oh also in either build going for a blink is also good but slows down your combat potential a lot for giving you ganking power(which is why QoP is a superior choice for either build in my opinion, built in blink > fiery soul by far).
Whenever I pick Lina though I'm generally the only support on the team so doing fancy shit isn't really possible, unless I don't care about winning anymore. Going combat lina when there's already 4 carries is pretty fucking pointless.