  We present Herschel-SPIRE Fourier Transform Spectrometer (FTS) and radio
follow-up observations of two Herschel-ATLAS (H-ATLAS) detected strongly lensed
distant galaxies. In one of the targeted galaxies H-ATLAS J090311.6+003906
(SDP.81) we detect [OIII] 88\mum and [CII] 158\mum lines at a signal-to-noise
ratio of ~5. We do not have any positive line identification in the other
fainter target H-ATLAS J091305.0-005343 (SDP.130). Currently SDP.81 is the
faintest sub-mm galaxy with positive line detections with the FTS, with
continuum flux just below 200 mJy in the 200-600 \mum wavelength range. The
derived redshift of SDP.81 from the two detections is z=3.043 +/-0.012, in
agreement with ground-based CO measurements. This is the first detection by
Herschel of the [OIII] 88\mum line in a galaxy at redshift higher than 0.05.
Comparing the observed lines and line ratios with a grid of photo-dissociation
region (PDR) models with different physical conditions, we derive the PDR cloud
density n ~ 2000 cm^{-3} and the far-UV ionizing radiation field G_0 ~ 200 (in
units of the Habing field -- the local Galactic interstellar radiation field of
1.6x10^{-6} W/m^2). Using the CO derived molecular mass and the PDR properties
we estimate the effective radius of the emitting region to be 500-700 pc. These
characteristics are typical for star-forming, high redshift galaxies. The radio
observations indicate that SDP.81 deviates significantly from the local
FIR/radio correlation, which hints that some fraction of the radio emission is
coming from an AGN. The constraints on the source size from millimiter-wave
observations put a very conservative upper limit of the possible AGN
contribution to less than 33%. These indications, together with the high
[OIII]/FIR ratio and the upper limit of [OI] 63\mum/[CII] 158\mum suggest that
some fraction of the ionizing radiation is likely to originate from an AGN.
