The WW2 Lithgow SMLE needs a magazine marked '4' on the rear spine.
Follower will be stamped '3' usually.
All this means it's set up for Mk7 ammunition

Any WW1 or WW2 #4 marked magazine will be a correct 'functional' replacement.
A Lithgow mfg magazine will be marked 'MA' on the spine also and probably have a Lithgow inspection mark or two there ( L/^/#).
NO serial number on the magazine,,only Ishapore India Arsenal #'d their magazines
Parkerized or blued finish,,which ever matches the rifle metal finish.

The LEC I (Lee Enfield CArbine Mark I) magazine is a 6 round capacity.
It is nothing more than a cut down standard 10 rd rifle magazine of the day from the MLE (Magazine Lee Enfield) or the MLM (Magazine Lee Metford)
These are 1890's era rifles and carbines.
The magazines differ from the #4 SMLE magazine above in that the SMLE uses a Z shaped spring inside,,the earlier LEC/MLE magazine uses a 'C' shaped spring. There's also a clip that fits over the front edge of the box on these, a different shape to the follower and the overall shape is slightly different as they used earlier Mk6 ammunition.
The SMLE magazines have a small flat spring rivited to the base of the spine to improve locking in position,,the earlier MLE/MLM magazines do not have this spring.
The LEC magazines,,,the mag body is too short for the spring to be an issue.

No serial number(s) on LEC magazines. Usually Arsenal inspector marks on the spine and a small loop
hard soldered to the front face for a short link chain to attach to the trigger guard for safe keeping.

If your Carbine DOES NOT accept a bayonet,,it is not an RIC (Royal Irish Constabulary) carbine, nor a New Zealand Carbine. Both of these versions were the only ones made that I know of that took a bayonet.
RIC and NZ carbines are usually stamped '1903' for their year of manufacture IIRC.
These two differ just a bit from each other. The RIC has a slimmer bbl and forend wood. It also has a muzzle ring to make up for the small dia bbl so the bayonet attaches firmly.

The earlier LEC I and the LEC I* do not have attachment to take a bayonet at all.
The '*' denotes the change made in May of 1899 that simply deleted the clearing rod from (all) British rifles and carbines.

The Lithgow marked SMLE magazine should not be too difficult to locate. Short of that, any #4 marked SMLE magazine will do a suitible replacement to function though most Lithgow buyers like the correct ones in place.
The LEC magazines can be tough to find but not impossible. They are not inexpensive when found.

Hope this helps..