I agree with Mei Mac it looks very similar to a Teleflex/Seastar CH2800, but the backing plate is different, so perhaps an earlier version. From a quick look the CH2800 seem out of stock or unlisted everywhere at the moment, but a more sustained search might find one. (Brace yourself for the price, though!)
Seastar is the new(-ish) brand name for Teleflex (following a takeover), but you will often still find them listed as Teleflex (check both names).
Apart from the aesthetics any brand/model side-mounting single lever Morse cable control (assuming that is what it is) will probably do, provided it (a) has the appropriate controls (presumably both engine and gear-change - i.e. 'dual function' - in your case?) and (b) is compatible with the type of cables you have (which are highly likely to be 33c type, which have a 3/16" thread on the cable ends).
The way the operator selects neutral on a dual function lever(which stops it being moved into gear when the throttle is operated forward or back) varies across makes and models - e.g. push button, pull out control lever, or twist knob on top (which is what I guess yours is) - but as far as the cables at the back are concerned it doesn't matter, the cables are pulled and pushed just the same.
Here's a selection of side-mounting single lever (n.b. both single - i.e. engine only - and dual function - i.e. both engine & gear change shown). Other suppliers and makes/models are available, I have no connection to ASAP other than as a satisfied customer). Search | ASAP Supplies