It's specifically NAVY commission (see below why I ask)?
Yes it is clearly a navy rank, the "command roster" says so:
"179 Astogator SDB3 (Naval Sublieutenant O2), Rgtal Ortillery Squadron, 4518th Lift Infantry Rgt"
Also, the marines know no sublieutenants (Book 4):
01: Second Lieutenant (Traveller rank 1 )
02: First Lieutenant (Traveller rank 1 )
...while the Navy does (Book 5):
02 Sublieutenant
(Quoting CT here, not T5)
Interestingly, the Fighter Pilots are indeed shown with Marine ranks, e.g.:
181 Pilot (Lieutenant O2), Rgtal Fighter Squadron, 4518th Lift Infantry Rgt
I reread the SMC and maybe pg. 41 gives an hint!?
"TEMPORARY DUTY
[...]
Imperial policy allows imperial marines to transfer to the 4518th (or other local units) for a limited period of time. While serving with a local unit (on temporary duty), the soldier is paid by the local unit and subject to local unit discipline.
[...]"
Maybe this policy also applies to the navy?