Say, I am in the open area, and have several access points in the vicinity, 500m or so. Laptop does not see the signal. Will something like LHG help to capture the signal and route to local devices?

Yes and No!! But yes some gain at least.

Yes high gain antenna will certainly help in receiving that access point (LHG, SXT, Disk, QRT, ....). But wifi is not like radio broadcast, it's not enough to receive the signal, the device must be able to answer, even if it is only for downloading things. The other direction, towards the access point, may be a weaker signal, but must be received and decoded by the other end.
Country regulation usually limits the signal level allowed to send! So your TX power is probably reduced to a legal limit. (27dBm, 30dBm, 20dBm (as TXpower dBm + antenna gain dBi) country dependent,) it is the same level as an Omnidirection AP, but at least it is better than your laptop (usually 14dBm), and certainly better than tablet or smartphone.

If the far away access point is using some high gain antenna also, all will be well balanced and the improvement is in both directions.

It depends............
If all are omni antennas not very likely, if one of the external ones is directional and you add a directional to your setup and aim it properly then yes.

For LHG XL 2 price tag I might give a try. Will let forum know..