Bounced LFO Instrument is off time, why?

Try *bounce in place* on the gated tracks so they're fixed in the arrange as audio before you bounce the full track down.

*Bounce in place* is new in Logic 9, if you have an earlier version then it won't be there.

Alternatively solo the track with the effect on it, set up the locators around that track and bounce the track from the master bounce button on the mixer (make sure that you have the add to Audio bin box checked ) Then grab the track you've just bounced from the audio bin and pull it back onto the arrange page and mute the original.

You could also freeze the track, but I prefer the bounce option.

Perhaps easier still... try bouncing the song in realtime rather than offline (if that's what you're doing). Many things like this in Logic sometimes don't work on offline bounces. But yes, Bill's suggestions are obviously the other way to go for a more thorough solution.

Is the LFO synced or free ? Is it set to retrigger or not?

Ok, hadn't read that it is the EXS, which doesn't have a retrigger on/off button for its LFO's. In this case it depends on which LFO (1 or 2) you actually use:

LFO 1 is a polyphonic LFO with key synchronization. This means that when LFO 1 is
used, each voice of the EXS24 has its own discrete LFO. When a note is played, the LFO
corresponding to that voice starts its cycle. This scheme means that the LFO cycles of
each voice played are not synchronous, and operate independently of each other. This
opens up a range of modulation possibilities. As an example—the LFO of one >voice
could generate the maximum modulation value, while the LFO assigned to another
voice could output its minimum value. This extremely flexible approach can result in
some very lively modulations.
In contrast, LFO 2 is a monophonic LFO without key synchronization. This means that
LFO 2 runs continuously, and is not restarted by the triggering of a new note. All voices
are modulated by the sole LFO, so the degree of modulation at any given time is the
same for all voices. This results in a rather synthetic-sounding modulation.

(from the Logic Studio Instruments and Effects pdf manual, p. 420)

Since LFO 1 is automatically synchronized with note events, your 'issue' must be with LFO 2.
It would help if you could post a screenshot of your EXS24, so I can see the settings.
And: are you sure there are no other modulations happening? Either via the EXS modulation matrix, or the samples themselves, or via insert- and send effects?

Bounce in realtime!